arXiv subjects

Subir Sachdev

Publications and source records attributed to Subir Sachdev.

At least 163 records · Page 9Linked to original sources

arXiv2017

Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the `anti-nodal' region of the square lattice Brillouin zone, and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin density wave mean field theory of the square lattice Hubbard model, and in a CP$^1$ theory of spinons. This theory leads to metals with an antinodal gap, and topological order which intertwines with precisely the observed broken symmetries.

cond-mat.str-el↗

arXiv2017

Critical behavior of an impurity at the boson superfluid-Mott insulator transition

We present a universal theory for the critical behavior of an impurity at the two-dimensional superfluid-Mott insulator transition. Our analysis is motivated by a numerical study of the Bose-Hubbard model with an impurity site by Huang et al. (Phys. Rev. B 94, 220502 (2016)), who found an impurity phase transition as a function of the trapping potential. The bulk theory is described by the $O(2)$ symmetric Wilson-Fisher conformal field theory, and we model the impurity by a localized spin-1/2 degree of freedom. We also consider a generalized model by considering an $O(N)$ symmetric bulk theory coupled to a spin-$S$ degree of freedom. We study this field theory using the $ε= 3 - d$ expansion, where the impurity-bulk interaction flows to an infrared stable fixed point at the critical trapping potential. We determine the scaling dimensions of the impurity degree of freedom and the associated critical exponents near the critical point. We also determine the universal contribution of the impurity to the finite temperature compressibility of the system at criticality. Our results are compared with recent numerical simulations.

cond-mat.quant-gas↗

arXiv2017

Quantum butterfly effect in weakly interacting diffusive metals

We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron field operators inherits a light-cone like growth, arising from an interplay of a growth (Lyapunov) exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder. In two spatial dimensions, the Lyapunov exponent is universally related at weak coupling to the sheet resistivity. We are able to define an effective temperature-dependent butterfly velocity, a speed limit for the propagation of quantum information, that is much slower than microscopic velocities such as the Fermi velocity and that is qualitatively similar to that of a quantum critical system with a dynamical critical exponent $z > 1$.

cond-mat.str-el↗

arXiv2017

Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions

We study thermal and electrical transport in metals and superconductors near a quantum phase transition where antiferromagnetic order disappears. The same theory can also be applied to quantum phase transitions involving the loss of certain classes of intrinsic topological order. For a clean superconductor, we recover and extend the well-known universal results. The heat conductivity for commensurate and incommensurate antiferromagnetism coexisting with superconductivity shows a markedly different doping dependence near the quantum critical point, thus allowing to distinguish the states. In the dirty limit, the results for the conductivities are qualitatively similar for the metal and the superconductor. In this regime, the geometric properties of the Fermi surface allow for a very good phenomenological understanding of the numerical results on the conductivities. In the simplest model, we find that the conductivities do not track the doping evolution of the Hall coefficient, in contrast to recent experimental findings. We propose a doping dependent scattering rate, possibly due to quenched short-range charge fluctuations below optimal doping, to consistently describe both the Hall data and the longitudinal conductivities.

cond-mat.str-el↗

arXiv2017

Spectrum of the Wilson-Fisher conformal field theory on the torus

We study the finite-size spectrum of the O($N$) symmetric Wilson-Fisher conformal field theory (CFT) on the $d=2$ spatial-dimension torus using the expansion in $ε=3-d$. This is done by deriving a set of universal effective Hamiltonians describing fluctuations of the zero momentum modes. The effective Hamiltonians take the form of $N$-dimensional quantum anharmonic oscillators, which are shown to be strongly coupled at the critical point for small $ε$. The low-energy spectrum is solved numerically for $N = 1,2,3,4$. Using exact diagonalization (ED), we also numerically study explicit lattice models known to be in the O($2$) and O($3$) universality class, obtaining estimates of the low-lying critical spectrum. The analytic and numerical results show excellent agreement and the critical low energy torus spectra are qualitatively different among the studied CFTs, identifying them as a useful fingerprint for detecting the universality class of a quantum critical point.

cond-mat.str-el↗

arXiv2017

Quantum quench of the Sachdev-Ye-Kitaev Model

We describe the non-equilibrium dynamics of the Sachdev-Ye-Kitaev models of fermions with all-to-all interactions. These provide tractable models of the dynamics of quantum systems without quasiparticle excitations. The Kadanoff-Baym equations show that the final state is thermal, and their numerical analysis appears consistent with a thermalization rate proportional to the absolute temperature of the final state. We also obtain an exact analytic solution of the non-equilibrium dynamics in the large $q$ limit of a model with $q$ fermion interactions: in this limit, the thermalization of the fermion Green's function is instantaneous.

cond-mat.str-el↗

arXiv2017

Thermal diffusivity and chaos in metals without quasiparticles

We study the thermal diffusivity $D_T$ in models of metals without quasiparticle excitations (`strange metals'). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infra-red fixed points $D_T$ is always related to parameters characterizing many-body quantum chaos: the butterfly velocity $v_B$, and Lyapunov time $τ_L$ through $D_T \sim v_B^2 τ_L$. The relationship holds independently of the charge density, periodic potential strength or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime, and is otherwise insensitive to the profile of any matter fields.

hep-th↗

arXiv2017

Insulators and metals with topological order and discrete symmetry breaking

Numerous experiments have reported discrete symmetry breaking in the high temperature pseudogap phase of the hole-doped cuprates, including breaking of one or more of lattice rotation, inversion, or time-reversal symmetries. In the absence of translational symmetry breaking or topological order, these conventional order parameters cannot explain the gap in the charged fermion excitation spectrum in the anti-nodal region. Zhao et al. (1601.01688) and Jeong et al. (arXiv:1701.06485) have also reported inversion and time-reversal symmetry breaking in insulating Sr2IrO4 similar to that in the metallic cuprates, but co-existing with Neel order. We extend an earlier theory of topological order in insulators and metals, in which the topological order combines naturally with the breaking of these conventional discrete symmetries. We find translationally-invariant states with topological order co-existing with both Ising-nematic order and spontaneous charge currents. The link between the discrete broken symmetries and the topological-order-induced pseudogap explains why the broken symmetries do not survive in the confining phases without a pseudogap at large doping. Our theory also connects to the O(3) non-linear sigma model and CP1 descriptions of quantum fluctuations of the Neel order. In this framework, the optimal doping criticality of the cuprates is primarily associated with the loss of topological order.

cond-mat.str-el↗

arXiv2017

QED$_3$ with quenched disorder: quantum critical states with interactions and disorder

Quantum electrodynamics in 2+1-dimensions (QED$_3$) is a strongly coupled conformal field theory (CFT) of a U(1) gauge field coupled to $2N$ two-component massless fermions. The $N=2$ CFT has been proposed as a ground state of the spin-1/2 kagome Heisenberg antiferromagnet. We study QED$_3$ in the presence of weak quenched disorder in its two spatial directions. When the disorder explicitly breaks the fermion flavor symmetry from SU($2N$)$\rightarrow$U(1)$\times$SU($N$) but preserves time-reversal symmetry, we find that the theory flows to a non-trivial fixed line at non-zero disorder with a continuously varying dynamical critical exponent $z>1$. We determine the zero-temperature flavor (spin) conductivity along the critical line. Our calculations are performed in the large-$N$ limit, and the disorder is handled using the replica method.

cond-mat.str-el↗

arXiv2017

Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography

We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number, $\mathcal{Q}$. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low temperature energy and $\mathcal{Q}$ fluctuations. We obtain higher-dimensional generalizations of the SYK models which display disordered metallic states without quasiparticle excitations, and we deduce their thermoelectric transport coefficients. We also examine the corresponding properties of Einstein-Maxwell-scalar theories on black brane geometries which interpolate from either AdS$_4$ or AdS$_5$ to an AdS$_2\times \mathbb{R}^2$ or AdS$_2\times \mathbb{R}^3$ near-horizon geometry. These provide holographic descriptions of non-quasiparticle metallic states without momentum conservation. We find a precise match between low temperature transport and thermodynamics of the SYK and holographic models. In both models the Seebeck transport coefficient is exactly equal to the $\mathcal{Q}$-derivative of the entropy. For the SYK models, quantum chaos, as characterized by the butterfly velocity and the Lyapunov rate, universally determines the thermal diffusivity, but not the charge diffusivity.

cond-mat.str-el↗

arXiv2017

Quantum chaos on a critical Fermi surface

We compute parameters characterizing many-body quantum chaos for a critical Fermi surface without quasiparticle excitations. We examine a theory of $N$ species of fermions at non-zero density coupled to a $U(1)$ gauge field in two spatial dimensions, and determine the Lyapunov rate and the butterfly velocity in an extended random-phase approximation. The thermal diffusivity is found to be universally related to these chaos parameters i.e. the relationship is independent of $N$, the gauge coupling constant, the Fermi velocity, the Fermi surface curvature, and high energy details.

cond-mat.str-el↗

arXiv2017

Supersymmetric SYK models

We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving $N$ Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The ${\cal N}=1$ model with a single supercharge has unbroken supersymmetry at large $N$, but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large $N$ equation, and also by performing numerical computations for small values of $N$. We also compute the large $N$ spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an ${\cal N}=2$ version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large $N$ computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.

hep-th↗

arXiv2017

Shear viscosity at the Ising-nematic quantum critical point in two dimensional metals

In an isotropic strongly interacting quantum liquid without quasiparticles, general scaling arguments imply that the dimensionless ratio $(k_B /\hbar)\, η/s$, where $η$ is the shear viscosity and $s$ is the entropy density, is a universal number. We compute the shear viscosity of the Ising-nematic critical point of metals in spatial dimension $d=2$ by an expansion below $d=5/2$. The anisotropy associated with directions parallel and normal to the Fermi surface leads to a violation of the scaling expectations: $η$ scales in the same manner as a chiral conductivity, and the ratio $η/s$ diverges at low temperature ($T$) as $T^{-2/z}$, where $z$ is the dynamic critical exponent for fermionic excitations dispersing normal to the Fermi surface.

cond-mat.str-el↗

arXiv2017

Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory

We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\infty$. Notably, for a semi-infinite cylindrical region it scales as $N^0$, in stark contrast to the $N$-linear result of the Gaussian fixed point.

cond-mat.str-el↗

arXiv2016

Holography of the Dirac Fluid in Graphene with two currents

Recent experiments have uncovered evidence of the strongly coupled nature of the graphene: the Wiedemann-Franz law is violated by up to a factor of 20 near the charge neutral point. We describe this strongly-coupled plasma by a holographic model in which there are two distinct conserved U(1) currents. We find that our analytic results for the transport coefficients for two current model have a significantly improved match to the density dependence of the experimental data than the models with only one current. The additive structure in the transports coefficients plays an important role. We also suggest the origin of the two currents.

hep-th↗

arXiv2016

The novel metallic states of the cuprates: Fermi liquids with topological order, and strange metals

This article is based on a talk by S.S. at the Nambu Memorial Symposium at the University of Chicago. We review ideas on the nature of the metallic states of the hole-doped cuprate high temperature superconductors, with an emphasis on the connections between the Luttinger theorem for the size of the Fermi surface, topological quantum field theories (TQFTs), and critical theories involving changes in the size of the Fermi surface. We begin with the derivation of the Luttinger theorem for a Fermi liquid, using momentum balance during a process of flux-insertion in a lattice electronic model with toroidal boundary conditions. We then review the TQFT of the Z2 spin liquid, and demonstrate its compatibility with the toroidal momentum balance argument. This discussion leads naturally to a simple construction of `topological' Fermi liquid states: the fractionalized Fermi liquid (FL*) and the algebraic charge liquid (ACL). We present arguments for a description of the pseudogap metal of the cuprates using Z2-FL* or Z2-ACL states with Ising-nematic order. These pseudogap metal states are also described as Higgs phases of a SU(2) gauge theory. The Higgs field represents local antiferromagnetism, but the Higgs-condensed phase does not have long-range antiferromagnetic order: the magnitude of the Higgs field determines the pseudogap, the reconstruction of the Fermi surface, and the Ising-nematic order. Finally, we discuss the route to the large Fermi surface Fermi liquid via the critical point where the Higgs condensate and Ising nematic order vanish, and the application of Higgs criticality to the strange metal.

cond-mat.str-el↗

arXiv2016

Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories

The low-energy spectra of many body systems on a torus, of finite size $L$, are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for 2+1D systems. Using a combination of analytical and numerical techniques, we show that the low-energy torus spectrum at criticality provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times $1/L$. We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a $Z_2$ topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides insight into the operator content of the critical field theory.

cond-mat.str-el↗

arXiv2016

Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal

Doping a Mott-insulating $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*). Such a phase has several favorable features that make it a candidate for the pseudogap metal for the underdoped cuprates. We focus on a particular, simple $\mathbb{Z}_2$-FL* state which can undergo a confinement transition to a spatially uniform superconductor which is smoothly connected to the `plain vanilla' BCS superconductor with $d$-wave pairing. Such a transition occurs by the condensation of bosonic particles carrying $+e$ charge but no spin (`chargons'). We show that modifying the dispersion of the bosonic chargons can lead to confinement transitions with charge density waves and pair density waves at the same wave-vector $\mathbf{K}$, co-existing with $d$-wave superconductivity. We also compute the evolution of the Hall number in the normal state during the transition from the plain vanilla FL* state to a Fermi liquid, and argue, following Coleman, Marston, and Schofield [Phys. Rev. B 72, 245111 (2005)], that it exhibits a discontinuous jump near optimal doping. We note the distinction between these results and those obtained from models of the pseudogap with fermionic chargons.

cond-mat.str-el↗