results for au:Mulligan_M in:cond-mat

- Mar 22 2018 cond-mat.str-el arXiv:1803.07767v1We consider the Hall conductivity of composite fermions in the presence of quenched disorder using the non-relativistic theory of Halperin, Lee and Read (HLR). Consistent with the recent analysis of Wang et al., we show that in a fully quantum mechanical transport calculation, the HLR theory, under suitable assumptions, exhibits a Hall response $\sigma_{xy}^{\rm CF} = - {1 \over 2} {e^2 \over h}$ that is consistent with an emergent particle-hole symmetric electrical response. Remarkably, this response of the HLR theory remains robust even when the disorder range is of the order of the Fermi wavelength.
- Mar 14 2018 cond-mat.str-el hep-th arXiv:1803.04418v1Gapped interfaces (and boundaries) of two-dimensional (2D) Abelian topological phases are shown to support a remarkably rich sequence of 1D symmetry-protected topological (SPT) states. We show that such interfaces can provide a physical interpretation for the corrections to the topological entanglement entropy of a 2D state with Abelian topological order found in Ref. 29. The topological entanglement entropy decomposes as $\gamma = \gamma_a + \gamma_s$, where $\gamma_a$ only depends on universal topological properties of the 2D state, while a non-zero correction $\gamma_s$ signals the emergence of the 1D SPT state that is produced by interactions along the entanglement cut and provides a direct measure of the stabilizing symmetry of the resulting SPT state. A correspondence is established between the possible values of $\gamma_s$ associated with a given interface - which is named Boundary Topological Entanglement Sequence - and classes of 1D SPT states. We show that symmetry-preserving domain walls along such 1D interfaces (or boundaries) generally host localized parafermion-like excitations that are stable to local symmetry-preserving perturbations.
- Dec 15 2017 cond-mat.str-el hep-th arXiv:1712.04942v2Although quantum Hall plateau transitions have been the prime examples of quantum criticality in a disordered electron system for the past three decades, many questions remain unanswered. Scaling of the measured electrical conductivity in the vicinity of these transitions reveals the surprising phenomenon of superuniversality where different transitions appear to share the same correlation length and dynamical critical exponent. Previous theoretical studies of these transitions within the framework of Abelian Chern-Simons theory coupled to matter found critical exponents that appear to directly depend on the change of the Hall conductivity across a specific phase transition, in contrast to what is observed experimentally. Here, we use non-Abelian bosonization and modular transformations to investigate theoretically the phenomenon of superuniversality. Specifically, we introduce a new effective theory that has an emergent $U(N)$ gauge symmetry with $N > 1$ for a quantum phase transition between an integer quantum Hall state and an insulator. We then use modular transformations to generate from this theory new effective descriptions for transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have Abelian statistics. In the 't Hooft large $N$ limit, the correlation length and dynamical critical exponents are independent of the particular transition. We argue that this superuniversality survives away from the large $N$ limit using recent duality conjectures.
- Nov 01 2017 cond-mat.str-el hep-th arXiv:1710.11137v2There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent $\nu \approx 2.3$ and that $\nu$ is observed to be super-universal, i.e., the same in the vicinity of distinct critical points. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with $U(N_c)$ gauge group coupled to $N_f = 1$ fermion. We study one class of theories in a controlled limit where $N_f \gg N_c$ and calculate $\nu$ to leading non-trivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent $\nu$ within the large $N_f \gg N_c$ expansion, they do offer a new parameter space of theories that is apparently different from prior works involving abelian Chern-Simons gauge fields.
- Sep 22 2017 cond-mat.str-el hep-th arXiv:1709.07005v1We study Dirac fermions in two spatial dimensions (2D) coupled to strongly fluctuating U(1) gauge fields in the presence of quenched disorder. Such systems are dual to theories of free Dirac fermions, which are vortices of the original theory. In analogy to superconductivity, when these fermionic vortices localize, the original system becomes a perfect conductor, and when the vortices possess a finite conductivity, the original fermions do as well. We provide several realizations of this principle and thereby introduce new examples of strongly interacting 2D metals that evade Anderson localization.
- Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\pm e^2/2h$ at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically as the electron density is varied about half-filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long wavelength physics.
- Sep 09 2016 hep-th cond-mat.str-el arXiv:1609.02149v2We study supersymmetry breaking perturbations of the simplest dual pair of 2+1-dimensional N = 2 supersymmetric field theories -- the free chiral multiplet and N = 2 super-QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several non-supersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these non-supersymmetric dualities directly descend.
- Aug 19 2016 hep-th cond-mat.str-el arXiv:1608.05077v1We study bosonization in 2+1 dimensions using mirror symmetry, a duality that relates pairs of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we dynamically obtain the bosonization duality that equates the theory of a free Dirac fermion to QED3 with a single scalar boson. This duality may be used to demonstrate the bosonization duality relating an $O(2)$-symmetric Wilson-Fisher fixed point to QED3 with a single Dirac fermion, Peskin-Dasgupta-Halperin duality, and the recently conjectured duality relating the theory of a free Dirac fermion to fermionic QED3 with a single flavor. Chern-Simons and BF couplings for both dynamical and background gauge fields play a central role in our approach. In the course of our study, we describe a chiral mirror pair that may be viewed as the minimal supersymmetric generalization of the two bosonization dualities.
- Jun 24 2016 hep-th cond-mat.str-el arXiv:1606.07067v1QCD with gauge group $SU(N_c)$ flows to an interacting conformal fixed point in three spacetime dimensions when the number of four-component Dirac fermions $N_f \gg N_c$. We study the stability of this fixed point via the $\epsilon$-expansion about four dimensions. We find that when the number of fermions is lowered to $N_f^{\rm crit} \approx {11 \over 2} N_c + (6 + {4 \over N_c}) \epsilon$, a certain four-fermion operator becomes relevant and the theory flows to a new infrared fixed point (massless or massive). F-theorem or entanglement monotonicity considerations complement our $\epsilon$-expansion calculation.
- May 27 2016 cond-mat.str-el hep-th arXiv:1605.08047v2We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed by Breznay et al. [PNAS 113, 280 (2016)] to exhibit particle-vortex symmetric electrical response, and the nearby metallic phase discovered earlier by Mason and Kapitulnik [Phys. Rev. Lett. 82, 5341 (1999)] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically-neutral Dirac fermion minimally coupled to an (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not require the introduction of disorder; rather, it results when the Dirac fermions exhibit vanishing Hall effect. The theory predicts approximately equal (diagonal) thermopower and Nernst signal with a deviation parameterized by the measured electrical Hall response at the symmetric point.
- Mar 21 2016 cond-mat.str-el hep-th arXiv:1603.05656v1We provide an effective description of a particle-hole symmetric state of electrons in a half-filled Landau level, starting from the traditional approach pioneered by Halperin, Lee and Read. Specifically, we study a system consisting of alternating quasi-one-dimensional strips of composite Fermi liquid (CFL) and composite hole liquid (CHL), both of which break particle-hole symmetry. When the CFL and CHL strips are identical in size, the resulting state is manifestly invariant under the combined action of a particle-hole transformation with respect to a single Landau level (which interchanges the CFL and CHL) and translation by one unit, equal to the strip width, in the direction transverse to the strips. At distances long compared to the strip width, we demonstrate that the system is described by a Dirac fermion coupled to an emergent gauge field, with an anti-unitary particle-hole symmetry, as recently proposed by Son.
- Sep 29 2015 cond-mat.str-el hep-th arXiv:1509.07865v1In several two-dimensional films that exhibit a magnetic field-tuned superconductor to insulator transition (SIT), stable metallic phases have been observed. Building on the `dirty boson' description of the SIT, we suggest that the metallic region is analogous to the composite Fermi liquid observed about half-filled Landau levels of the two-dimensional electron gas. The composite fermions here are mobile vortices attached to one flux quantum of an emergent gauge field. The composite vortex liquid is a 2D non-Fermi liquid metal, which we argue is stable to weak quenched disorder. We describe several experimental consequences of the emergent composite vortex liquid.
- Sep 16 2015 cond-mat.str-el hep-th arXiv:1509.04280v2We define a `hyperconductor' to be a material whose electrical and thermal DC conductivities are infinite at zero temperature and finite at any non-zero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially-gap-generating interactions and potentially-localizing disorder. In this paper, we compute the low-temperature DC and AC electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter $\Delta_X$, is a power law, $\sigma \propto 1/T^{1 - 2(2-\Delta_X)}$ when $\Delta_X \geq 2$, down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which $\Delta_X = 2$ and $\Delta_X \approx 2$ for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high-temperatures, followed by an exponential increase of the conductivity $\ln \sigma \sim 1/T$ at intermediate temperatures and, finally, $\sigma \propto 1/T^{2-2(2-{\Delta_X})}$ at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.
- Jun 05 2015 cond-mat.str-el hep-th arXiv:1506.01376v2We study the dynamics of the half-filled zeroth Landau level of Dirac fermions using mirror symmetry, a supersymmetric duality between certain pairs of $2+1$-dimensional theories. We show that the half-filled zeroth Landau level of a pair of Dirac fermions is dual to a pair of Fermi surfaces of electrically-neutral composite fermions, coupled to an emergent gauge field. Thus, we use supersymmetry to provide a derivation of flux attachment and the emergent Fermi liquid-like state for the lowest Landau level of Dirac fermions. We find that in the dual theory the Coulomb interaction induces a dynamical exponent $z=2$ for the emergent gauge field, making the interactions classically marginal. This enables us to map the problem of $2+1$-dimensional Dirac fermions in a finite transverse magnetic field, interacting via a strong Coulomb interaction, into a perturbatively controlled model. We analyze the resulting low-energy theory using the renormalization group and determine the nature of the BCS interaction in the emergent composite Fermi liquid.
- Feb 20 2015 cond-mat.str-el hep-th arXiv:1502.05404v2The half-filled Landau level is widely believed to be described by the Halperin-Lee-Read theory of the composite Fermi liquid (CFL). In this paper, we develop a theory for the particle-hole conjugate of the CFL, the Anti-CFL, which we argue to be a distinct phase of matter as compared with the CFL. The Anti-CFL provides a possible explanation of a recent experiment [Kamburov et. al., Phys. Rev. Lett. 113, 196801 (2014)] demonstrating that the density of composite fermions in GaAs quantum wells corresponds to the electron density when the filling fraction $\nu < 1/2$ and to the hole density when $\nu > 1/2$. We introduce a local field theory for the CFL and Anti-CFL in the presence of a boundary, which we use to study CFL - Insulator - CFL junctions, and the interface between the Anti-CFL and CFL. We show that the CFL - Anti-CFL interface allows partially fused boundary phases in which "composite electrons" can directly tunnel into "composite holes," providing a non-trivial example of transmutation between topologically distinct quasiparticles. We discuss several observable consequences of the Anti-CFL, including a predicted resistivity jump at a first order transition between uniform CFL and Anti-CFL phases. We also present a theory of a continuous quantum phase transition between the CFL and Anti-CFL. We conclude that particle-hole symmetry requires a modified view of the half-filled Landau level, in the presence of strong electron-electron interactions and weak disorder, as a critical point between the CFL and the Anti-CFL.
- Nov 21 2014 cond-mat.str-el hep-th arXiv:1411.5369v3A given fractional quantum Hall state may admit multiple, distinct edge phases on its boundary. We explore the implications that multiple edge phases have for the entanglement spectrum and entropy of a given bulk state. We describe the precise manner in which the entanglement spectrum depends upon local (tunneling) interactions along an entanglement cut and throughout the bulk. The sensitivity to local conditions near the entanglement cut appears not only in gross features of the spectrum, but can also manifest itself in an additive, positive constant correction to the topological entanglement entropy, i.e., it increases its magnitude. A natural interpretation for this result is that the tunneling interactions across an entanglement cut can function as a barrier to certain types of quasiparticle transport across the cut, thereby, lowering the total entanglement between the two regions.
- Apr 18 2014 cond-mat.str-el arXiv:1404.4367v2We show that a 1D quantum wire with $23$ channels of interacting fermions has a perfect metal phase in which all weak perturbations that could destabilize this phase are irrelevant. Consequently, weak disorder does not localize it, a weak periodic potential does not open a gap, and contact with a superconductor also fails to open a gap. Similar phases occur for $N \geq 24$ channels of fermions, except for $N=25$, and for $8k$ channels of interacting bosons, with $k\geq 3$. Arrays of perfect metallic wires form higher-dimensional fermionic or bosonic perfect metals, albeit highly-anisotropic ones.
- Nov 04 2013 cond-mat.str-el hep-th arXiv:1311.0285v2We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to $2 e^2/h$ and vanishing thermal Hall conductivity. In contrast to the integer quantum Hall state of fermions, a point contact can have a dramatic effect on the low energy physics. In the absence of disorder, a point contact generically leads to a partially-split Hall bar geometry. We describe the resulting intermediate fixed point via the two-terminal electrical (Hall) conductance of the edge modes. Disorder along the edge, however, both restores the universality of the two-terminal conductance and helps preserve the integrity of the Hall bar within the relevant parameter regime.
- The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at $\nu=8$ and 12, with experimentally-testable consequences. We show that this can occur in Abelian fractional quantum Hall states as well, with the simplest examples being at $\nu=8/7, 12/11, 8/15, 16/5$. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. Edge phases correspond to lattices while bulk phases correspond to genera of lattices. Since there are typically multiple lattices in a genus, the bulk-edge correspondence is typically one-to-many; there are usually many stable fully chiral edge phases corresponding to the same bulk. We explain these correspondences using the theory of integral quadratic forms. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers $p$ in which every quasiparticle has a topological spin that is a $p^n$-th root of unity for some $n$. It also leads to a simple demonstration that all Abelian topological phases can be represented by $U(1)^N$ Chern-Simons theory parameterized by a K-matrix.
- Apr 03 2013 cond-mat.str-el hep-th arXiv:1304.0772v2We consider states of bosons in two dimensions that do not support anyons in the bulk, but nevertheless have stable chiral edge modes that are protected even without any symmetry. Such states must have edge modes with central charge $c=8k$ for integer $k$. While there is a single such state with $c=8$, there are, naively, two such states with $c=16$, corresponding to the two distinct even unimodular lattices in 16 dimensions. However, we show that these two phases are the same in the bulk, which is a consequence of the uniqueness of signature $(8k +n, n)$ even unimodular lattices. The bulk phases are stably equivalent, in a sense that we make precise. However, there are two different phases of the edge corresponding to these two lattices, thereby realizing a novel form of the bulk-edge correspondence. Two distinct fully chiral edge phases are associated with the same bulk phase, which is consistent with the uniqueness of the bulk since the transition between them, which is generically first-order, can occur purely at the edge. Our construction is closely related to $T$-duality of toroidally compactified heterotic strings. We discuss generalizations of these results.
- Jan 19 2013 cond-mat.str-el hep-th arXiv:1301.4230v1The surface of a 3+1d topological insulator hosts an odd number of gapless Dirac fermions when charge conjugation and time-reversal symmetries are preserved. Viewed as a purely 2+1d system, this surface theory would necessarily explicitly break parity and time-reversal when coupled to a fluctuating gauge field. Here we explain why such a state can exist on the boundary of a 3+1d system without breaking these symmetries, even if the number of boundary components is odd. This is accomplished from two complementary perspectives: topological quantization conditions and regularization. We first discuss the conditions under which (continuous) large gauge transformations may exist when the theory lives on a boundary of a higher-dimensional spacetime. Next, we show how the higher-dimensional bulk theory is essential in providing a parity-invariant regularization of the theory living on the lower-dimensional boundary or defect.
- Apr 04 2011 cond-mat.str-el hep-th arXiv:1104.0256v2We present a Landau-Ginzburg theory for a fractional quantized Hall nematic state and the transition to it from an isotropic fractional quantum Hall state. This justifies Lifshitz-Chern-Simons theory -- which is shown to be its dual -- on a more microscopic basis and enables us to compute a ground state wave function in the symmetry-broken phase. In such a state of matter, the Hall resistance remains quantized while the longitudinal DC resistivity due to thermally-excited quasiparticles is anisotropic. We interpret recent experiments at Landau level filling factor \nu =7/3 in terms of our theory.
- Oct 29 2010 cond-mat.str-el hep-th arXiv:1010.6094v2We study how the \theta -term is affected by interactions in certain one-dimensional gapped systems that preserve charge-conjugation, parity, and time-reversal invariance. We exploit the relation between the chiral anomaly of a fermionic system and the classical shift symmetry of its bosonized dual. The vacuum expectation value of the dual boson is identified with the value of the \theta -term for the corresponding fermionic system. Two (related) examples illustrate the identification. We first consider the massive Luttinger liquid and find the \theta -term to be insensitive to the strength of the interaction. Next, we study the continuum limit of the Heisenberg XXZ spin-1/2 chain, perturbed by a second nearest-neighbor spin interaction. For a certain range of the XXZ anisotropy, we find that we can tune between two distinct sets of topological phases by varying the second nearest-neighbor coupling. In the first, we find the standard vacua at \theta = 0, \pi, while the second contains vacua that spontaneously break charge-conjugation and parity with fractional \theta / \pi = 1/ 2, 3/2. We also study quantized pumping in both examples following recent work.
- Apr 21 2010 cond-mat.str-el hep-th arXiv:1004.3570v2We study a novel abelian gauge theory in 2+1 dimensions which has surprising theoretical and phenomenological features. The theory has a vanishing coefficient for the square of the electric field $e_i^2$, characteristic of a quantum critical point with dynamical critical exponent $z=2$, and a level-$k$ Chern-Simons coupling, which is \it marginal at this critical point. For $k=0$, this theory is dual to a free $z=2$ scalar field theory describing a quantum Lifshitz transition, but $k \neq 0$ renders the scalar description non-local. The $k \neq 0$ theory exhibits properties intermediate between the (topological) pure Chern-Simons theory and the scalar theory. For instance, the Chern-Simons term does not make the gauge field massive. Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary, and a non-trivial ground state degeneracy $k^g$ when it is placed on a finite-size Riemann surface of genus $g$. The coefficient of $e_i^2$ is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. We compute zero-temperature transport coefficients in both phases and at the critical point, and comment briefly on the relevance of our results to recent experiments.
- We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that, under quite general conditions, the entanglement entropy of a large and simply connected sub-system of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory.
- Aug 14 2008 hep-th cond-mat.str-el arXiv:0808.1725v2We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent $z$, which governs the anisotropy between spatial and temporal scaling $t \to \lambda^z t$, $x \to \lambda x$; we focus on the case with $z=2$. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.
- Oct 25 2007 hep-th cond-mat.stat-mech arXiv:0710.4348v2The boundary entropy log(g) of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g due to a slightly relevant bulk perturbation and find that it has no preferred sign. The boundary entropy log(g) can therefore increase during appropriate bulk flows. This is demonstrated explicitly in flows between minimal models. We discuss the applications of this result to D-branes in string theory and to impurity problems in condensed matter.