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SciPost Physics

SciPost Physics Vol. 9 issue 1 (July 2020)

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Entanglement islands in higher dimensions

Ahmed Almheiri, Raghu Mahajan, Jorge E. Santos

SciPost Phys. 9, 001 (2020) · published 1 July 2020 | · pdf

It has been suggested in recent work that the Page curve of Hawking radiation can be recovered using computations in semi-classical gravity provided one allows for "islands" in the gravity region of quantum systems coupled to gravity. The explicit computations so far have been restricted to black holes in two-dimensional Jackiw-Teitelboim gravity. In this note, we numerically construct a five-dimensional asymptotically AdS geometry whose boundary realizes a four-dimensional Hartle-Hawking state on an eternal AdS black hole in equilibrium with a bath. We also numerically find two types of extremal surfaces: ones that correspond to having or not having an island. The version of the information paradox involving the eternal black hole exists in this setup, and it is avoided by the presence of islands. Thus, recent computations exhibiting islands in two-dimensional gravity generalize to higher dimensions as well.
Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas

Giuseppe Del Vecchio Del Vecchio, Alvise Bastianello, Andrea De Luca, Giuseppe Mussardo

SciPost Phys. 9, 002 (2020) · published 6 July 2020 | · pdf

We study the out-of-equilibrium properties of a classical integrable non-relativistic theory, with a time evolution initially prepared with a finite energy density in the thermodynamic limit. The theory considered here is the Non-Linear Schrodinger equation which describes the dynamics of the one-dimensional interacting Bose gas in the regime of high occupation numbers. The main emphasis is on the determination of the late-time Generalised Gibbs Ensemble (GGE), which can be efficiently semi-numerically computed on arbitrary initial states, completely solving the famous quench problem in the classical regime. We take advantage of known results in the quantum model and the semiclassical limit to achieve new exact results for the momenta of the density operator on arbitrary GGEs, which we successfully compare with ab-initio numerical simulations. Furthermore, we determine the whole probability distribution of the density operator (full counting statistics), whose exact expression is still out of reach in the quantum model.
Rigorous bounds on dynamical response functions and time-translation symmetry breaking

Marko Medenjak, Tomaz Prosen, Lenart Zadnik

SciPost Phys. 9, 003 (2020) · published 7 July 2020 | · pdf

Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e. extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.
Equilibration of quantum cat states

Tony Jin

SciPost Phys. 9, 004 (2020) · published 8 July 2020 | · pdf

We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in the mean, there exists a remnant of the initial quantum coherences visible in the strength of the fluctuations of the steady state. We back-up our analysis with numerical results obtained on the XXX spin chain with a random field along the z-axis in the ergodic regime and find good qualitative and quantitative agreement with the theory. We also present and discuss a framework where equilibrium quantities can be computed from general statistical ensembles without relying on microscopic details about the initial state, akin to the eigenstate thermalization hypothesis.
A systematic interpolatory method for an impurity in a one-dimensional fermionic background

Erik J. Lindgren, Rafael E. Barfknecht, Nikolaj T. Zinner

SciPost Phys. 9, 005 (2020) · published 13 July 2020 | · pdf

We explore a new numerical method for studying one-dimensional quantum systems in a trapping potential. We focus on the setup of an impurity in a fermionic background, where a single distinguishable particle interacts through a contact potential with a number of identical fermions. We can accurately describe this system, for various particle numbers, different trapping potentials and arbitrary finite repulsion, by constructing a truncated basis containing states at both zero and infinite repulsion. The results are compared with matrix product states methods and with the analytical result for two particles in a harmonic well.
Hall viscosity and conductivity of two-dimensional chiral superconductors

Félix Rose, Omri Golan, Sergej Moroz

SciPost Phys. 9, 006 (2020) · published 14 July 2020 | · pdf

We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chiral superconductors, where fermions pair due to a short-range attractive potential, e.g. $p+\mathrm{i}p$ pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chiral superconductors, where the Coulomb potential decays as inverse distance, we find an intermediate behavior between intrinsic two-dimensional superconductors and superfluids. These results are obtained by means of both effective and microscopic field theory.
Universal bounds on transport in holographic systems with broken translations

Matteo Baggioli, Wei-Jia Li

SciPost Phys. 9, 007 (2020) · published 15 July 2020 | · pdf

We study the presence of universal bounds on transport in homogeneous holographic models with broken translations. We verify numerically that, in holographic systems with momentum dissipation, the viscosity to entropy bound might be violated but the shear diffusion constant remains bounded by below. This confirms the idea that $\eta/s$ loses its privileged role in non-relativistic systems and that, in order to find more universal bounds, one should rather look at diffusion constants. We strengthen this idea by showing that, in presence of spontaneously broken translations, the Goldstone diffusion constant satisfies a universal lower bound in terms of the Planckian relaxation time and the butterfly velocity. Additionally, all the diffusive processes in the model satisfy an upper bound, imposed by causality, which is given in terms of the thermalization time -- the imaginary part of the first non-hydrodynamic mode in the spectrum -- and the speed of longitudinal sound. Finally, we discuss the existence of a bound on the speed of sound in holographic conformal solids and we show that the conformal value acts as a lower (and not upper) bound on the speed of longitudinal phonons. Nevertheless, we show that the stiffness $\partial p/\partial \epsilon$ is still bounded by above by its conformal value. This suggests that the bounds conjectured in the past have to be considered on the stiffness of the system, related to its equation of state, and not on the propagation speed of sound.
Skyrmions, Quantum Hall Droplets, and one current to rule them all

Avner Karasik

SciPost Phys. 9, 008 (2020) · published 20 July 2020 | · pdf

We introduce a novel Skyrme-like conserved current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The associated charge is equivalent to the skyrmion charge for any smooth configuration. In addition, there exist singular configurations that can be identified as N_f=1 baryons charged under the new symmetry. Under this identification, the vector mesons play the role of the Chern-Simons vector fields living on the quantum Hall droplet that forms the N_f=1 baryon. We propose that this current is the correct effective expression for the baryon current at low energies. This proposal gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. In addition, Chern-Simons dualities on the droplet can be interpreted as a result of Seiberg-like duality between gluons and vector mesons.
Normal modes in thermal AdS via the Selberg zeta function

Victoria L. Martin, Andrew Svesko

SciPost Phys. 9, 009 (2020) · published 21 July 2020 | · pdf

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin $s$ fields on hyperbolic quotient spacetimes $\mathbb{H}^{3}/\mathbb{Z}$ are related via the Selberg zeta function. We extend that analysis to thermal $\text{AdS}_{2n+1}$ backgrounds, with quotient structure $\mathbb{H}^{2n+1}/\mathbb{Z}$. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.
Topological superconductors on superstring worldsheets

Justin Kaidi, Julio Parra-Martinez, Yuji Tachikawa, with a mathematical appendix by Arun Debray

SciPost Phys. 9, 010 (2020) · published 21 July 2020 | · pdf

We point out that different choices of Gliozzi-Scherk-Olive (GSO) projections in superstring theory can be conveniently understood by the inclusion of fermionic invertible phases, or equivalently topological superconductors, on the worldsheet. This allows us to find that the unoriented Type $\rm 0$ string theory with $\Omega^2=(-1)^{\sf f}$ admits different GSO projections parameterized by $n$ mod 8, depending on the number of Kitaev chains on the worldsheet. The presence of $n$ boundary Majorana fermions then leads to the classification of D-branes by $KO^n(X)\oplus KO^{-n}(X)$ in these theories, which we also confirm by the study of the D-brane boundary states. Finally, we show that there is no essentially new GSO projection for the Type $\rm I$ worldsheet theory by studying the relevant bordism group, which classifies corresponding invertible phases. This paper provides the details for the results announced in the letter \cite{Kaidi:2019pzj}.
Relaxation and entropy generation after quenching quantum spin chains

Máté Lencses, Octavio Pomponio, Gabor Takacs

SciPost Phys. 9, 011 (2020) · published 22 July 2020 | · pdf

This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving R\'enyi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum.
Critical energy landscape of linear soft spheres

Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani

SciPost Phys. 9, 012 (2020) · published 23 July 2020 | · pdf

We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are non-linear, system spanning, and characterized by a set of non-trivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that self-organize into new, critical, marginally stable, states.
Critical properties of a comb lattice

Natalia Chepiga, Steven R. White

SciPost Phys. 9, 013 (2020) · published 27 July 2020 | · pdf

In this paper we study the critical properties of the Heisenberg spin-1/2 model on a comb lattice -- a 1D backbone decorated with finite 1D chains -- the teeth. We address the problem numerically by a comb tensor network that duplicates the geometry of a lattice. We observe a fundamental difference between the states on a comb with even and odd number of sites per tooth, which resembles an even-odd effect in spin-1/2 ladders. The comb with odd teeth is always critical, not only along the teeth, but also along the backbone, which leads to a competition between two critical regimes in orthogonal directions. In addition, we show that in a weak-backbone limit the excitation energy scales as $1/(NL)$, and not as $1/N$ or $1/L$ typical for 1D systems. For even teeth in the weak backbone limit the system corresponds to a collection of decoupled critical chains of length $L$, while in the strong backbone limit, one spin from each tooth forms the backbone, so the effective length of a critical tooth is one site shorter, $L-1$. Surprisingly, these two regimes are connected via a state where a critical chain spans over two nearest neighbor teeth, with an effective length $2L$.
Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases

Lukas Rammelmüller, Joaquín E. Drut, Jens Braun

SciPost Phys. 9, 014 (2020) · published 28 July 2020 | · pdf

We study spin- and mass-imbalanced mixtures of spin-$\tfrac{1}{2}$ fermions interacting via an attractive contact potential in one spatial dimension. Specifically, we address the influence of unequal particle masses on the pair formation by means of the complex Langevin method. By computing the pair-correlation function and the associated pair-momentum distribution we find that inhomogeneous pairing is present for all studied spin polarizations and mass imbalances. To further characterize the pairing behavior, we analyze the density-density correlations in momentum space, the so-called shot noise, which is experimentally accessible through time-of-flight imaging. At finite spin polarization, the latter is known to show distinct maxima at momentum configurations associated with the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) instability. Besides those maxima, we find that additional features emerge in the noise correlations when mass imbalance is increased, revealing the stability of FFLO-type correlations against mass imbalance and furnishing an experimentally accessible signature to probe this type of pairing.
Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps

Tobias Gulden, Erez Berg, Mark S. Rudner, Netanel H. Lindner

SciPost Phys. 9, 015 (2020) · published 29 July 2020 | · pdf

We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.