Publications

Order by: publication date number of citations

• Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

  Dung Xuan Nguyen, Andrey Gromov, Sergej Moroz

  SciPost Phys. 9, 076 (2020) · published 19 November 2020 | Toggle abstract · pdf

  Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

  34 citations

• Many-body quantum dynamics slows down at low density

  Xiao Chen, Yingfei Gu, Andrew Lucas

  SciPost Phys. 9, 071 (2020) · published 12 November 2020 | Toggle abstract · pdf

  We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective operator size at finite chemical potential through suitably regularized out-of-time-ordered correlation functions. The growth rate of this density-dependent operator size vanishes algebraically with charge density; hence we obtain new bounds on Lyapunov exponents and butterfly velocities in charged systems at a given density, which are parametrically stronger than any Lieb-Robinson bound. We argue that the density dependence of our bound on the Lyapunov exponent is saturated in the charged Sachdev-Ye-Kitaev model. We also study random automaton quantum circuits and Brownian Sachdev-Ye-Kitaev models, each of which exhibit a different density dependence for the Lyapunov exponent, and explain the discrepancy. We propose that our results are a cartoon for understanding Planckian-limited energy-conserving dynamics at finite temperature.

  23 citations

• Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair hopping

  Iman Mahyaeh, Jurriaan Wouters, Dirk Schuricht

  SciPost Phys. Core 3, 011 (2020) · published 12 November 2020 | Toggle abstract · pdf

  We study a tight binding model of $\mathbb{Z}_3$-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge $c=2$, and two gapless phases with central charge $c=1$. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

  4 citations

• Studying dynamics in two-dimensional quantum lattices using tree tensor network states

  Benedikt Kloss, David R. Reichman, Yevgeny Bar Lev

  SciPost Phys. 9, 070 (2020) · published 11 November 2020 | Toggle abstract · pdf

  We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle in a manifold of binary and quaternary Tree Tensor Network States. The approach is found to be competitive with existing matrix product state approaches. We discuss issues related to the convergence of the method, which could be relevant to a broader set of numerical techniques used for the study of two-dimensional systems.

  13 citations

• The quantum entropy cone of hypergraphs

  Ning Bao, Newton Cheng, Sergio Hernández-Cuenca, Vincent P. Su

  SciPost Phys. 9, 067 (2020) · published 10 November 2020 | Toggle abstract · pdf

  In this work, we generalize the graph-theoretic techniques used for the holographic entropy cone to study hypergraphs and their analogously-defined entropy cone. This allows us to develop a framework to efficiently compute entropies and prove inequalities satisfied by hypergraphs. In doing so, we discover a class of quantum entropy vectors which reach beyond those of holographic states and obey constraints intimately related to the ones obeyed by stabilizer states and linear ranks. We show that, at least up to 4 parties, the hypergraph cone is identical to the stabilizer entropy cone, thus demonstrating that the hypergraph framework is broadly applicable to the study of entanglement entropy. We conjecture that this equality continues to hold for higher party numbers and report on partial progress on this direction. To physically motivate this conjectured equivalence, we also propose a plausible method inspired by tensor networks to construct a quantum state from a given hypergraph such that their entropy vectors match.

  14 citations

• The vacua of dipolar cavity quantum electrodynamics

  Michael Schuler, Daniele De Bernardis, Andreas M. Läuchli, Peter Rabl

  SciPost Phys. 9, 066 (2020) · published 9 November 2020 | Toggle abstract · pdf

  The structure of solids and their phases is mainly determined by static Coulomb forces while the coupling of charges to the dynamical, i.e., quantized degrees of freedom of the electromagnetic field plays only a secondary role. Recently, it has been speculated that this general rule can be overcome in the context of cavity quantum electrodynamics (QED), where the coupling of dipoles to a single field mode can be dramatically enhanced. Here we present a first exact analysis of the ground states of a dipolar cavity QED system in the non-perturbative coupling regime, where electrostatic and dynamical interactions play an equally important role. Specifically, we show how strong and long-range vacuum fluctuations modify the states of dipolar matter and induce novel phases with unusual properties. Beyond a purely fundamental interest, these general mechanisms can be important for potential applications, ranging from cavity-assisted chemistry to quantum technologies based on ultrastrongly coupled circuit QED systems.

  24 citations

• Separation of variables bases for integrable $gl_{\mathcal{M}|\mathcal{N}}$ and Hubbard models

  Jean Michel Maillet, Giuliano Niccoli, Louis Vignoli

  SciPost Phys. 9, 060 (2020) · published 27 October 2020 | Toggle abstract · pdf

  We construct quantum Separation of Variables (SoV) bases for both the fundamental inhomogeneous $gl_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model both defined with quasi-periodic twisted boundary conditions given by twist matrices having simple spectrum. The SoV bases are obtained by using the integrable structure of these quantum models,i.e. the associated commuting transfer matrices, following the general scheme introduced in [1]; namely, they are given by set of states generated by the multiple action of the transfer matrices on a generic co-vector. The existence of such SoV bases implies that the corresponding transfer matrices have non degenerate spectrum and that they are diagonalizable with simple spectrum if the twist matrices defining the quasi-periodic boundary conditions have that property. Moreover, in these SoV bases the resolution of the transfer matrix eigenvalue problem leads to the resolution of the full spectral problem, i.e. both eigenvalues and eigenvectors. Indeed, to any eigenvalue is associated the unique (up to a trivial overall normalization) eigenvector whose wave-function in the SoV bases is factorized into products of the corresponding transfer matrix eigenvalue computed on the spectrum of the separate variables. As an application, we characterize completely the transfer matrix spectrum in our SoV framework for the fundamental $gl_{1|2}$ supersymmetric integrable model associated to a special class of twist matrices. From these results we also prove the completeness of the Bethe Ansatz for that case. The complete solution of the spectral problem for fundamental inhomogeneous $gl_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model under the general twisted boundary conditions will be addressed in a future publication.

  10 citations

• Relaxation of bosons in one dimension and the onset of dimensional crossover

  Chen Li, Tianwei Zhou, Igor Mazets, Hans-Peter Stimming, Frederik S. Møller, Zijie Zhu, Yueyang Zhai, Wei Xiong, Xiaoji Zhou, Xuzong Chen, Jörg Schmiedmayer

  SciPost Phys. 9, 058 (2020) · published 22 October 2020 | Toggle abstract · pdf

  We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newton's cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.

  21 citations

• Bistabilities and domain walls in weakly open quantum systems

  Florian Lange, Achim Rosch

  SciPost Phys. 9, 057 (2020) · published 21 October 2020 | Toggle abstract · pdf

  Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $\epsilon$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $\sim 1/\sqrt{\epsilon}$ while the density of domain walls is exponentially small in $1/\sqrt{\epsilon}$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.

• Kibble–Zurek mechanism in the Ising Field Theory

  Kristóf Hódsági, Marton Kormos

  SciPost Phys. 9, 055 (2020) · published 20 October 2020 | Toggle abstract · pdf

  The Kibble-Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble-Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.

  16 citations