arXiv subjects

Paolo Glorioso

Publications and source records attributed to Paolo Glorioso.

32 records · Page 2Linked to original sources

arXiv2020

Gauging anomalous unitary operators

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as C and CP, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.

cond-mat.str-el↗

arXiv2020

Hydrodynamics in lattice models with continuous non-Abelian symmetries

We develop a systematic effective field theory of hydrodynamics for many-body systems on the lattice with global continuous non-Abelian symmetries. Models with continuous non-Abelian symmetries are ubiquitous in physics, arising in diverse settings ranging from hot nuclear matter to cold atomic gases and quantum spin chains. In every dimension and for every flavor symmetry group, the low energy theory is a set of coupled noisy diffusion equations. Independence of the physics on the choice of canonical or microcanonical ensemble is manifest in our hydrodynamic expansion, even though the ensemble choice causes an apparent shift in quasinormal mode spectra. We use our formalism to explain why flavor symmetry is qualitatively different from hydrodynamics with other non-Abelian conservation laws, including angular momentum and charge multipoles. As a significant application of our framework, we study spin and energy diffusion in classical one-dimensional SU(2)-invariant spin chains, including the Heisenberg model along with multiple generalizations. We argue based on both numerical simulations and our effective field theory framework that non-integrable spin chains on a lattice exhibit conventional spin diffusion, in contrast to some recent predictions that diffusion constants grow logarithmically at late times. We show that the apparent enhancement of diffusion is due to slow equilibration caused by (non-Abelian) hydrodynamic fluctuations.

cond-mat.stat-mech↗

arXiv2020

Breakdown of Diffusion on the Edge

We show that dirty Quantum Hall systems exhibit large hydrodynamic fluctuations at their edge that lead to anomalously damped charge excitations in the Kardar-Parisi-Zhang universality class $ω\simeq ck - i \mathcal D k^{3/2} $. The dissipative optical conductivity of the edge is singular at low frequencies $σ(ω) \sim 1/ω^{1/3}$. These results are direct consequences of the charge continuity relation, the chiral anomaly, and thermalization on the edge -- in particular translation invariance is not assumed. Diffusion of heat similarly breaks down, with a universality class that depends on whether the bulk thermal Hall conductivity vanishes. We further establish the theory of fluctuating hydrodynamics for surface chiral metals, where charge fluctuations give logarithmic corrections to transport.

cond-mat.str-el↗

arXiv2019

Effective response theory for Floquet topological systems

We present an effective field theory approach to the topological response of Floquet systems with symmetry group $G$. This is achieved by introducing a background $G$ gauge field in the Schwinger-Keldysh formalism, which is suitable for far from equilibrium systems. We carry out this program for chiral topological Floquet systems (anomalous Floquet-Anderson insulators) in two spatial dimensions, and the group cohomology models of topological Floquet unitaries. These response actions serve as many-body topological invariants for topological Floquet unitaries. The effective action approach also leads us to propose novel topological response functions.

cond-mat.str-el↗

arXiv2018

A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems

We develop a prescription for computing real-time correlation functions defined on a Schwinger-Keldysh contour for non-equilibrium systems using gravity. The prescription involves a new analytic continuation procedure in a black hole geometry which can be dynamical. For a system with a slowly varying horizon, the continuation enables computation of the Schwinger-Keldysh generating functional using derivative expansion, drastically simplifying calculations. We illustrate the prescription with two-point functions for a scalar operator. We then use it to derive from gravity the recently proposed non-equilibrium effective action for diffusion.

hep-th↗

arXiv2018

Effective field theory of magnetohydrodynamics from generalized global symmetries

We introduce an effective action for non-dissipative magnetohydrodynamics. A crucial guiding principle is the generalized global symmetry of electrodynamics, which naturally leads to introducing a "dual photon" as the degree of freedom responsible for the electromagnetic component of the fluid. The formalism includes additional degrees of freedom and symmetries which characterize the hydrodynamic regime. By suitably enhancing one of the symmetries, the theory becomes force-free electrodynamics. The symmetries furthermore allow to systematize local and non-local conserved helicities. We also discuss higher-derivative corrections.

hep-th↗

arXiv2018

Lectures on non-equilibrium effective field theories and fluctuating hydrodynamics

We review recent progress in developing effective field theories (EFTs) for non-equilibrium processes at finite temperature, including a new formulation of fluctuating hydrodynamics, and a new proof of the second law of thermodynamics. There are a number of new elements in formulating EFTs for such systems. Firstly, the nature of IR variables is very different from those of a system in equilibrium or near the vacuum. Secondly, while all static properties of an equilibrium system can in principle be extracted from the partition function, there appears no such quantity which can capture all non-equilibrium properties. Thirdly, non-equilibrium processes often involve dissipation, which is notoriously difficult to deal with using an action principle. The purpose of the review is to explain how to address these issues in a pedagogic manner, with fluctuating hydrodynamics as a main example.

hep-th↗

arXiv2018

Ghostbusters: Unitarity and Causality of Non-equilibrium Effective Field Theories

For a non-equilibrium physical system defined along a closed time path (CTP), a key constraint is the so-called largest time equation, which is a consequence of unitarity and implies causality. In this paper, we present a simple proof that if the propagators of a non-equilibrium effective action have the proper pole structure, the largest time equation is obeyed to all loop orders. Ghost fields and BRST symmetry are not needed. In particular, the arguments for the proof can also be used to show that if ghost fields are introduced, their contributions vanish.

hep-th↗

arXiv2017

Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions

We derive effective actions for parity-violating fluids in both $(3+1)$ and $(2+1)$ dimensions, including those with anomalies. As a corollary we confirm the most general constitutive relations for such systems derived previously using other methods. We discuss in detail connections between parity-odd transport and underlying discrete symmetries. In (3+1) dimensions we elucidate connections between anomalous transport coefficients and global anomalies, and clarify a previous puzzle concerning transports and local gravitational anomalies.

hep-th↗

arXiv2017

Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current

In this paper we further develop the fluctuating hydrodynamics proposed in arXiv:1511.03646 in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a $Z_2$ symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physically equivalent to the previously proposed local KMS condition in the classical limit, but is more convenient to implement and more general. It is applicable to any states in local equilibrium rather than just thermal density matrix perturbed by external background fields. Finally we elaborate the formulation for a conformal fluid, which contains some new features, and work out the explicit form of the entropy current to second order in derivatives for a neutral conformal fluid.

hep-th↗

arXiv2017

The second law of thermodynamics from symmetry and unitarity

The second law of thermodynamics states that for a thermally isolated system entropy never decreases. Most physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger than microscopic molecular collision scales and thus can be considered as in local equilibrium. For a many-body system in local equilibrium a stronger version of the second law applies which says that the entropy production at each spacetime point should be non-negative. In this paper we provide a proof of the second law for such systems and a first derivation of the local second law. For this purpose we develop a general non-equilibrium effective field theory of slow degrees of freedom from integrating out fast degrees of freedom in a quantum many-body system and consider its classical limit. The key elements of the proof are the presence of a $Z_2$ symmetry, which can be considered as a proxy for local equilibrium and micro-time-reversibility, and a classical remnant of quantum unitarity. The $Z_2$ symmetry leads to a local current from a procedure analogous to that used in the Noether theorem. Unitarity leads to a definite sign of the divergence of the current. We also discuss the origin of an arrow of time, as well as the coincidence of causal and thermodynamical arrows of time. Applied to hydrodynamics, the proof gives a first-principle derivation of the phenomenological entropy current condition and provides a constructive procedure for obtaining the entropy current.

hep-th↗

arXiv2017

Effective field theory of dissipative fluids

We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional $Z_2$ symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.

hep-th↗

arXiv2017

Classification of certain asymptotically AdS space-times with Ricci-flat boundary

We classify solutions to Einstein's equations in AdS with Ricci-flat boundary metric and with covariantly constant boundary stress tensor, which in general is not diagonalizable, i.e. it does not admit a reference frame. New solutions are found, and in the context of the AdS/CFT duality they should describe a boundary QFT in certain non-equilibrium steady states. Further imposing the absence of scalar curvature singularities leads to a subset of metrics that can be seen as null deformations of AdS or of the AdS soliton. We also outline the procedure of solving the equations when a scalar is coupled to the metric, which holographically leads to non-Lorentz-invariant RG flows.

gr-qc↗

arXiv2015

Off-shell hydrodynamics from holography

We outline a program for obtaining an action principle for dissipative fluid dynamics by considering the holographic Wilsonian renormalization group applied to systems with a gravity dual. As a first step, in this paper we restrict to systems with a non-dissipative horizon. By integrating out gapped degrees of freedom in the bulk gravitational system between an asymptotic boundary and a horizon, we are led to a formulation of hydrodynamics where the dynamical variables are not standard velocity and temperature fields, but the relative embedding of the boundary and horizon hypersurfaces. At zeroth order, this action reduces to that proposed by Dubovsky et al. as an off-shell formulation of ideal fluid dynamics.

hep-th↗