arXiv subjects

Max A. Metlitski

Publications and source records attributed to Max A. Metlitski.

At least 37 records · Page 2Linked to original sources

arXiv2015

The half-filled Landau level: the case for Dirac composite fermions

One of the most spectacular experimental findings in the fractional quantum Hall effect is evidence for an emergent Fermi surface when the electron density is nearly half the density of magnetic flux quanta ($ν= 1/2$). The seminal work of Halperin, Lee, and Read (HLR) first predicted that at $ν= 1/2$ composite fermions--bound states of an electron and a pair of vortices--experience zero net magnetic field and can form a "composite Fermi liquid" with an emergent Fermi surface. In this paper we use infinite cylinder DMRG to provide compelling numerical evidence for the existence of a Fermi sea of composite fermions for realistic interactions between electrons at $ν= 1/2$. Moreover, we show that the state is particle-hole symmetric, in contrast to the construction of HLR. Instead, our findings are consistent if the composite fermions are massless Dirac particles, at finite density, similar to the surface state of a 3D topological insulator. Exploiting this analogy we devise a numerical test and successfully observe the suppression of $2k_F$ backscattering characteristic of Dirac particles.

cond-mat.str-el↗

arXiv2015

Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators

Particle-vortex duality is a powerful theoretical tool that has been used to study bosonic systems. Here we propose an analogous duality for Dirac fermions in 2+1 dimensions. The physics of a single Dirac cone is proposed to be described by a dual theory, QED3 with a dual Dirac fermion coupled to a gauge field. This duality is established by considering two alternate descriptions of the 3d topological insulator (TI) surface. The first description is the usual Dirac cone surface state. The second description is accessed via an electric-magnetic duality of the bulk TI coupled to a gauge field, which maps it to a gauged topological superconductor. This alternate description ultimately leads to a new surface theory - dual QED3. The dual theory provides an explicit derivation of the T-Pfaffian state, a proposed surface topological order of the TI, which is simply the paired superfluid state of the dual fermions. The roles of time reversal and particle-hole symmetry are exchanged by the duality, which connects some of our results to a recent conjecture by Son on particle-hole symmetric quantum Hall states.

cond-mat.str-el↗

arXiv2015

Are non-Fermi-liquids stable to Cooper pairing?

States of matter with a sharp Fermi-surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include: ${\it (i)}$ quantum critical points associated with the onset of order in metals; ${\it (ii)}$ spinon Fermi-surface (U(1) spin-liquid) state of a Mott insulator; ${\it (iii)}$ Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi-liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of a phase transition in a metal, and demonstrate that the attractive interaction mediated by the order parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi-surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between ${\it (i)}$ $U(1)$ and $Z_2$ spin-liquid states; ${\it (ii)}$ Halperin-Lee-Read and Moore-Read states.

cond-mat.str-el↗

arXiv2015

Entanglement Entropy of Systems with Spontaneously Broken Continuous Symmetry

We study entanglement properties of systems with spontaneously broken continuous symmetry. We find that in addition to the expected area law behavior, the entanglement entropy contains a subleading contribution which diverges logarithmically with the subsystem size in agreement with the Monte Carlo simulations of A. Kallin et. al. (Phys. Rev. B 84, 165134 (2011)). The coefficient of the logarithm is a universal number given simply by $N_G (d-1)/2$, where $N_G$ is the number of Goldstone modes and $d$ is the spatial dimension. This term is present even when the subsystem boundary is straight and contains no corners, and its origin lies in the interplay of Goldstone modes and restoration of symmetry in a finite volume. We also compute the "low-energy" part of the entanglement spectrum and show that it has the same characteristic "tower of states" form as the physical low-energy spectrum obtained when a system with spontaneously broken continuous symmetry is placed in a finite volume.

cond-mat.str-el↗

arXiv2014

Interaction effects on 3D topological superconductors: surface topological order from vortex condensation, the 16 fold way and fermionic Kramers doublets

Three dimensional topological superconductors with time reversal symmetry (class DIII) are indexed by an integer $ν$, the number of surface Majorana cones, according to the free fermion classification. The superfluid B phase of He$^3$ realizes the $ν=1$ phase. Recently, it has been argued that this classification is reduced in the presence of interactions to Z$_{16}$. This was argued from the symmetry respecting surface topological orders of these states, which provide a non-perturbative definition of the bulk topological phase. Here, we verify this conclusion by focusing on the even index case, $ν=2m$, where a vortex condensation approach can be used to explicitly derive the surface topological orders. We show a direct relation to the well known result on one dimensional topological superconductors (class BDI), where interactions reduce the free fermion classification from Z down to Z$_8$. Finally, we discuss in detail the fermionic analog of Kramers time reversal symmetry, which allows semions of some surface topological orders to transform as $T^2=\pm i$.

cond-mat.str-el↗

arXiv2013

A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators

A 3d electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this paper we deduce a symmetry-respecting, gapped surface termination of an ETI, which carries an intrinsic 2d topological order, Moore-Read x anti-semion. The Moore-Read sector supports non-Abelian charge 1/4 anyons, while the Abelian, anti-semion sector is electrically neutral. Time-reversal symmetry is implemented in this surface phase in a highly non-trivial way. Moreover, it is impossible to realize this phase strictly in 2d, simultaneously preserving its implementation of both the particle number and time-reversal symmetries. A 1d edge on the ETI surface between the topologically-ordered phase and the topologically trivial time-reversal-broken phase with a Hall conductivity sigma_H = 1/2, carries a right-moving neutral Majorana mode, a right-moving bosonic charge mode and a left-moving bosonic neutral mode. The topologically-ordered phase is separated from the surface superconductor by a direct second order phase transition in the XY* universality class, which is driven by the condensation of a charge 1/2 boson, when approached from the topologically-ordered side, and proliferation of a flux 4π-vortex, when approached from the superconducting side. In addition, we prove that time-reversal invariant (interacting) electron insulators with no intrinsic topological order and electromagnetic response characterized by a θ-angle, θ= π, do not exist if the electrons transform as Kramers singlets under time-reversal.

cond-mat.str-el↗

arXiv2013

Bosonic topological insulator in three dimensions and the statistical Witten effect

It is well-known that one signature of the three-dimensional electron topological insulator is the Witten effect: if the system is coupled to a compact electromagnetic gauge field, a monopole in the bulk acquires a half-odd-integer polarization charge. In the present work, we propose a corresponding phenomenon for the topological insulator of bosons in 3d protected by particle number conservation and time-reversal symmetry. We claim that although a monopole inside a topological insulator of bosons can remain electrically neutral, its statistics are transmuted from bosonic to fermionic. We demonstrate that this ``statistical Witten effect" directly implies that if the surface of the topological insulator is neither gapless, nor spontaneously breaks the symmetry, it necessarily supports an intrinsic two-dimensional topological order. Moreover, the surface properties cannot be fully realized in a purely 2d system. We also confirm that the surface phases of the bosonic topological insulator proposed by Vishwanath and Senthil (arXiv:1209.3058) provide a consistent termination of a bulk exhibiting the statistical Witten effect. In a companion paper, we will provide an explicit field-theoretic, lattice-regularized, construction of the 3d topological insulator of bosons, employing a parton decomposition and subsequent condensation of parton-monopole composites.

cond-mat.str-el↗

arXiv2012

Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals

The quantum theory of antiferromagnetism in metals is necessary for our understanding of numerous intermetallic compounds of widespread interest. In these systems, a quantum critical point emerges as external parameters (such as chemical doping) are varied. Because of the strong coupling nature of this critical point, and the "sign problem" plaguing numerical quantum Monte Carlo (QMC) methods, its theoretical understanding is still incomplete. Here, we show that the universal low-energy theory for the onset of antiferromagnetism in a metal can be realized in lattice models, which are free from the sign problem and hence can be simulated efficiently with QMC. Our simulations show Fermi surface reconstruction and unconventional spin-singlet superconductivity across the critical point.

cond-mat.str-el↗

arXiv2012

Orthogonal Metals: The simplest non-Fermi liquids

We present a fractionalized metallic phase which is indistinguishable from the Fermi liquid in conductivity and thermodynamics, but is sharply distinct in one electron properties, such as the electron spectral function. We dub this phase the `Orthogonal Metal.' The Orthogonal Metal and the transition to it from the Fermi liquid are naturally described using a slave particle representation wherein the electron is expressed as a product of a fermion and a slave Ising spin. We emphasize that when the slave spins are disordered the result is not a Mott insulator (as erroneously assumed in the prior literature) but rather the Orthogonal Metal. We construct prototypical ground state wavefunctions for the Orthogonal Metal by modifying the Jastrow factor of Slater-Jastrow wavefunctions that describe ordinary Fermi liquids. We further demonstrate that the transition from the Fermi liquid to the Orthogonal Metal can, in some circumstances, provide a simple example of a continuous destruction of a Fermi surface with a critical Fermi surface appearing right at the critical point. We present exactly soluble models that realize an Orthogonal Metal phase, and the phase transition to the Fermi liquid. These models thus provide valuable solvable examples for phase transitions associated with the death of a Fermi surface.

cond-mat.str-el↗

arXiv2012

Antiferromagnetism in metals: from the cuprate superconductors to the heavy fermion materials

The critical theory of the onset of antiferromagnetism in metals, with concomitant Fermi surface reconstruction, has recently been shown to be strongly coupled in two spatial dimensions. The onset of unconventional superconductivity near this critical point is reviewed: it involves a subtle interplay between the breakdown of fermionic quasiparticle excitations on the Fermi surface, and the strong pairing glue provided by the antiferromagnetic fluctuations. The net result is a logarithm-squared enhancement of the pairing vertex for generic Fermi surfaces, with a universal dimensionless co-efficient independent of the strength of interactions, which is expected to lead to superconductivity at the scale of the Fermi energy. We also discuss the possibility that the antiferromagnetic critical point can be replaced by an intermediate `fractionalized Fermi liquid' phase, in which there is Fermi surface reconstruction but no long-range antiferromagnetic order. We discuss the relevance of this phase to the underdoped cuprates and the heavy-fermion materials.

cond-mat.str-el↗

arXiv2011

Quantum critical response at the onset of spin density wave order in two-dimensional metals

We study the frequency dependence of the electron self energy and the optical conductivity in a recently developed field theory of the spin density wave quantum phase transition in two dimensional metals. We focus on the interplay between the Fermi surface `hot spots' and the remainder of the `cold' Fermi surface. Scattering of electrons off the fluctuations of the spin density order parameter, ϕ, is strongest at the hot spots; we compute the conductivity due to this scattering in a rainbow approximation. We point out the importance of composite operators, built out of products of the primary electron or $ϕ$ fields: these have important effects also away from the hot spots. The simplest composite operator, ϕ^2, leads to non-Fermi liquid behavior on the entire Fermi surface. We also find an intermediate frequency window in which the cold electrons loose their quasiparticle form due to effectively one-dimensional scattering processes. The latter processes are part of umklapp scattering which leads to singular contributions to the optical conductivity at the lowest frequencies at zero temperature.

cond-mat.str-el↗

arXiv2010

Instabilities near the onset of spin density wave order in metals

We discuss the low energy theory of two-dimensional metals near the onset of spin density wave order. It is well known that such a metal has a superconducting instability induced by the formation of spin-singlet pairs of electrons, with the pairing amplitude changing sign between regions of the Fermi surface connected by the spin density wave ordering wavevector. Here we review recent arguments that there is an additional instability which is nearly as strong: towards the onset of a modulated bond order which is locally an Ising-nematic order. This new instability is a consequence of an emergent "pseudospin" symmetry of the low energy theory---the symmetry maps the sign-changing pairing amplitude to the bond order parameter.

cond-mat.supr-con↗

arXiv2010

Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order

We present a renormalization group theory for the onset of Ising-nematic order in a Fermi liquid in two spatial dimensions. This is a quantum phase transition, driven by electron interactions, which spontaneously reduces the point-group symmetry from square to rectangular. The critical point is described by an infinite set of 2+1 dimensional local field theories, labeled by points on the Fermi surface. Each field theory contains a real scalar field representing the Ising order parameter, and fermionic fields representing a time-reversed pair of patches on the Fermi surface. We demonstrate that the field theories obey compatibility constraints required by our redundant representation of the underlying degrees of freedom. Scaling forms for the response functions are proposed, and supported by computations by up to three loops. Extensions of our results to other transitions of two-dimensional Fermi liquids with broken point-group and/or time-reversal symmetry are noted. Our results extend also to the problem of a Fermi surface coupled to a U(1) gauge field.

cond-mat.str-el↗

arXiv2010

Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order

We present a field-theoretic renormalization group analysis of Abanov and Chubukov's model of the spin density wave transition in two dimensional metals. We identify the independent field scale and coupling constant renormalizations in a local field theory, and argue that the damping constant of spin density wave fluctuations tracks the renormalization of the local couplings. The divergences at two-loop order overdetermine the renormalization constants, and are shown to be consistent with our renormalization scheme. We describe the physical consequences of our renormalization group equations, including the breakdown of Fermi liquid behavior near the "hot spots" on the Fermi surface. In particular, we find that the dynamical critical exponent z receives corrections to its mean-field value z = 2. At higher orders in the loop expansion, we find infrared singularities similar to those found by S.-S. Lee for the problem of a Fermi surface coupled to a gauge field. A treatment of these singularities implies that an expansion in 1/N, (where N is the number of fermion flavors) fails for the present problem. We also discuss the renormalization of the pairing vertex, and find an enhancement which scales as logarithm-squared of the energy scale. A similar enhancement is also found for a modulated bond order which is locally an Ising-nematic order.

cond-mat.str-el↗

arXiv2009

Fluctuating spin density waves in metals

Recent work has used a U(1) gauge theory to describe the physics of Fermi pockets in the presence of fluctuating spin density wave order. We generalize this theory to an arbitrary band structure and ordering wavevector. The transition to the large Fermi surface state, without pockets induced by local spin density wave order, is described by embedding the U(1) gauge theory in a SU(2) gauge theory. The phase diagram of the SU(2) gauge theory shows that the onset of spin density wave order in the Fermi liquid occurs either directly, in the framework discussed by Hertz, or via intermediate non-Fermi liquid phases with Fermi surfaces of fractionalized excitations. We discuss application of our results to the phase diagram of the cuprates.

cond-mat.str-el↗

arXiv2009

Entanglement Entropy in the O(N) model

It is generally believed that in spatial dimension d > 1 the leading contribution to the entanglement entropy S = - tr rho_A log rho_A scales as the area of the boundary of subsystem A. The coefficient of this "area law" is non-universal. However, in the neighbourhood of a quantum critical point S is believed to possess subleading universal corrections. In the present work, we study the entanglement entropy in the quantum O(N) model in 1 < d < 3. We use an expansion in epsilon = 3-d to evaluate i) the universal geometric correction to S for an infinite cylinder divided along a circular boundary; ii) the universal correction to S due to a finite correlation length. Both corrections are different at the Wilson-Fisher and Gaussian fixed points, and the epsilon -> 0 limit of the Wilson-Fisher fixed point is distinct from the Gaussian fixed point. In addition, we compute the correlation length correction to the Renyi entropy S_n = (log tr rho^n_A)/(1-n) in epsilon and large-N expansions. For N -> infinity, this correction generally scales as N^2 rather than the naively expected N. Moreover, the Renyi entropy has a phase transition as a function of n for d close to 3.

cond-mat.stat-mech↗

arXiv2008

Monopoles in CP(N-1) model via the state-operator correspondence

One of the earliest proposed phase transitions beyond the Landau-Ginzburg-Wilson paradigm is the quantum critical point separating an antiferromagnet and a valence-bond-solid on a square lattice. The low energy description of this transition is believed to be given by the 2+1 dimensional CP(1) model -- a theory of bosonic spinons coupled to an abelian gauge field. Monopole defects of the gauge field play a prominent role in the physics of this phase transition. In the present paper, we use the state-operator correspondence of conformal field theory in conjunction with the 1/N expansion to study monopole operators at the critical fixed point of the CP(N-1) model. This elegant method reproduces the result for monopole scaling dimension obtained through a direct calculation by Murthy and Sachdev. The technical simplicity of our approach makes it the method of choice when dealing with monopole operators in a conformal field theory.

cond-mat.str-el↗

arXiv2008

Imaging bond order near non-magnetic impurities in square lattice antiferromagnets

We study the textures of generalized "charge densities" (scalar objects invariant under time reversal), in the vicinity of non-magnetic impurities in square-lattice quantum anti-ferromagnets, by order parameter field theories. Our central finding is the structure of the "vortex" in the generalized density wave order parameter centered at the non-magnetic impurity. Using exact numerical data from quantum Monte Carlo simulations on an antiferromagnetic spin model, we are able to verify the results of our field theoretic study. We extend our phenomenological approach to the period-4 bond-centered density wave found in the underdoped cuprates.

cond-mat.str-el↗