Publications

Order by: publication date number of citations

• Topological lattice models with constant Berry curvature

  Daniel Varjas, Ahmed Abouelkomsan, Kang Yang, Emil J. Bergholtz

  SciPost Phys. 12, 118 (2022) · published 6 April 2022 | Toggle abstract · pdf

  Band geometry plays a substantial role in topological lattice models. The Berry curvature, which resembles the effect of magnetic field in reciprocal space, usually fluctuates throughout the Brillouin zone. Motivated by the analogy with Landau levels, constant Berry curvature has been suggested as an ideal condition for realizing fractional Chern insulators. Here we show that while the Berry curvature cannot be made constant in a topological two-band model, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. However, contrary to the intuitive expectation, we find that making the Berry curvature constant does not always improve the properties of fractional Chern insulator states. In fact, we show that an "ideal flatband" cannot have constant Berry curvature, equivalently, we show that the density algebra of Landau levels cannot be realised in any tight-binding lattice system.

  20 citations

• Information Scrambling with Conservation Laws

  Jonah Kudler-Flam, Ramanjit Sohal, Laimei Nie

  SciPost Phys. 12, 117 (2022) · published 4 April 2022 | Toggle abstract · pdf

  The delocalization or scrambling of quantum information has emerged as a central ingredient in the understanding of thermalization in isolated quantum many-body systems. Recently, significant progress has been made analytically by modeling non-integrable systems as stochastic systems, lacking a Hamiltonian picture, while honest Hamiltonian dynamics are frequently limited to small system sizes due to computational constraints. In this paper, we address this by investigating the role of conservation laws (including energy conservation) in the thermalization process from an information-theoretic perspective. For general non-integrable models, we use the equilibrium approximation to show that the maximal amount of information is scrambled (as measured by the tripartite mutual information of the time-evolution operator) at late times even when a system conserves energy. In contrast, we explicate how when a system has additional symmetries that lead to degeneracies in the spectrum, the amount of information scrambled must decrease. This general theory is exemplified in case studies of holographic conformal field theories (CFTs) and the Sachdev-Ye-Kitaev (SYK) model. Due to the large Virasoro symmetry in 1+1D CFTs, we argue that, in a sense, these holographic theories are not maximally chaotic, which is explicitly seen by the non-saturation of the second R\'enyi tripartite mutual information. The roles of particle-hole and U(1) symmetries in the SYK model are milder due to the degeneracies being only two-fold, which we confirm explicitly at both large- and small-$N$. We reinterpret the operator entanglement in terms the growth of local operators, connecting our results with the information scrambling described by out-of-time-ordered correlators, identifying the mechanism for suppressed scrambling from the Heisenberg perspective.

  11 citations

• Universal Deformations

  Aleksey Cherman, Theodore Jacobson, Maria Neuzil

  SciPost Phys. 12, 116 (2022) · published 1 April 2022 | Toggle abstract · pdf

  QFTs with local topological operators feature unusual sectors called "universes," which are separated by infinite-tension domain walls. We show that such systems have relevant deformations with exactly-calculable effects. These deformations allow one to dial the vacuum energy densities of the universes. We describe applications of these deformations to confinement in 2d gauge theories, as well as a curious violation of the effective field theory naturalness principle.

  20 citations

• Tails of Instability and Decay: a Hydrodynamic Perspective

  Olalla A. Castro-Alvaredo, Cecilia De Fazio, Benjamin Doyon, Aleksandra A. Ziółkowska

  SciPost Phys. 12, 115 (2022) · published 31 March 2022 | Toggle abstract · pdf

  In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and life-time of the particle, observed in scattering events. In this paper, we uncover new, dynamical signatures of unstable excitations and show that they have a strong effect on the non-equilibrium properties of QFT. Focusing on a 1+1D integrable model, and using the theory of Generalized Hydrodynamics, we study the formation and decay of unstable particles by analysing the release of hot matter into a low-temperature environment. We observe the formation of tails and the decay of the emitted nonlinear waves, in sharp contrast to the situation without unstable excitations. We also uncover a new phenomenon by which a wave of a stable population of unstable particles may persist without decay for long times. We expect these signatures of the presence of unstable particles to have a large degree of universality. Our study shows that the out-of-equilibrium dynamics of many-body systems can be strongly affected not only by the spectrum, but also by excitations with finite life-times.

  3 citations

• Gravitational wave induced baryon acoustic oscillations

  Christian Döring, Salvador Centelles Chuliá, Manfred Lindner, Bjoern Malte Schaefer, Matthias Bartelmann

  SciPost Phys. 12, 114 (2022) · published 31 March 2022 | Toggle abstract · pdf

  We study the impact of gravitational waves originating from a first order phase transition on structure formation. To do so, we perform a second order perturbation analysis in the $1+3$ covariant framework and derive a wave equation in which second order, adiabatic density perturbations of the photon-baryon fluid are sourced by the gravitational wave energy density during radiation domination and on sub-horizon scales. The scale on which such waves affect the energy density perturbation spectrum is found to be proportional to the horizon size at the time of the phase transition times its inverse duration. Consequently, structure of the size of galaxies and bigger can only be affected in this way by relatively late phase transitions at $\ge 10^{6}\,\text{s}$. Using cosmic variance as a bound we derive limits on the strength $\alpha$ and the relative duration $(\beta/H_*)^{-1}$ of phase transitions as functions of the time of their occurrence which results in a new exclusion region for the energy density in gravitational waves today. We find that the cosmic variance bound forbids only relative long lasting phase transitions, e.g. $\beta/H_*\lesssim 6.8$ for $t_*\approx 5\times10^{11}\,\text{s}$, which exhibit a substantial amount of supercooling $\alpha>20$ to affect the matter power spectrum.

  3 citations

• Mechanisms for the emergence of Gaussian correlations

  Marek Gluza, Thomas Schweigler, Mohammadamin Tajik, João Sabino, Federica Cataldini, Frederik S. Møller, Si-Cong Ji, Bernhard Rauer, Jörg Schmiedmayer, Jens Eisert, Spyros Sotiriadis

  SciPost Phys. 12, 113 (2022) · published 30 March 2022 | Toggle abstract · pdf

  We comprehensively investigate two distinct mechanisms leading to memory loss of non-Gaussian correlations after switching off the interactions in an isolated quantum system undergoing out-of-equilibrium dynamics. The first mechanism is based on spatial scrambling and results in the emergence of locally Gaussian steady states in large systems evolving over long times. The second mechanism, characterized as `canonical transmutation', is based on the mixing of a pair of canonically conjugate fields, one of which initially exhibits non-Gaussian fluctuations while the other is Gaussian and dominates the dynamics, resulting in the emergence of relative Gaussianity even at finite system sizes and times. We evaluate signatures of the occurrence of the two candidate mechanisms in a recent experiment that has observed Gaussification in an atom-chip controlled ultracold gas and elucidate evidence that it is canonical transmutation rather than spatial scrambling that is responsible for Gaussification in the experiment. Both mechanisms are shown to share the common feature that the Gaussian correlations revealed dynamically by the quench are already present though practically inaccessible at the initial time. On the way, we present novel observations based on the experimental data, demonstrating clustering of equilibrium correlations, analyzing the dynamics of full counting statistics, and utilizing tomographic reconstructions of quantum field states. Our work aims at providing an accessible presentation of the potential of atom-chip experiments to explore fundamental aspects of quantum field theories in quantum simulations.

  3 citations

• Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice

  Matías G. Gonzalez, Bernard Bernu, Laurent Pierre, Laura Messio

  SciPost Phys. 12, 112 (2022) · published 30 March 2022 | Toggle abstract · pdf

  The spin-$\frac12$ triangular lattice antiferromagnetic Heisenberg model has been for a long time the prototypical model of magnetic frustration. However, only very recently this model has been proposed to be realized in the Ba$_8$CoNb$_6$O$_{24}$ compound. The ground-state and thermodynamic properties are evaluated from a high-temperature series expansions interpolation method, called "entropy method", and compared to experiments. We find a ground-state energy $e_0 = -0.5445(2)$ in perfect agreement with exact diagonalization results. We also calculate the specific heat and entropy at all temperatures, finding a good agreement with the latest experiments, and evaluate which further interactions could improve the comparison. We explore the spatially anisotropic triangular lattice and provide evidence that supports the existence of a gapped spin liquid between the square and triangular lattices.

  7 citations

• Quantum Gutzwiller approach for the two-component Bose-Hubbard model

  Victor E. Colussi, Fabio Caleffi, Chiara Menotti, Alessio Recati

  SciPost Phys. 12, 111 (2022) · published 29 March 2022 | Toggle abstract · pdf

  We study the effects of quantum fluctuations in the two-component Bose-Hubbard model generalizing to mixtures the quantum Gutzwiller approach introduced recently in [Phys. Rev. Research 2, 033276 (2020)]. As a basis for our study, we analyze the mean-field ground-state phase diagram and spectrum of elementary excitations, with particular emphasis on the quantum phase transitions of the model. Within the quantum critical regimes, we address both the superfluid transport properties and the linear response dynamics to density and spin probes of direct experimental relevance. Crucially, we find that quantum fluctuations have a dramatic effect on the drag between the superfluid species of the system, particularly in the vicinity of the paired and antipaired phases absent in the usual one-component Bose-Hubbard model. Additionally, we analyse the contributions of quantum corrections to the one-body coherence and density/spin fluctuations from the perspective of the collective modes of the system, providing results for the few-body correlations in all the regimes of the phase diagram.

  9 citations

• Flowing bosonization in the nonperturbative functional renormalization-group approach

  Romain Daviet, Nicolas Dupuis

  SciPost Phys. 12, 110 (2022) · published 28 March 2022 | Toggle abstract · pdf

  Bosonization allows one to describe the low-energy physics of one-dimensional quantum fluids within a bosonic effective field theory formulated in terms of two fields: the "density" field $\varphi$ and its conjugate partner, the phase $\vartheta$ of the superfluid order parameter. We discuss the implementation of the nonperturbative functional renormalization group in this formalism, considering a Luttinger liquid in a periodic potential as an example. We show that in order for $\vartheta$ and $\varphi$ to remain conjugate variables at all energy scales, one must dynamically redefine the field $\vartheta$ along the renormalization-group flow. We derive explicit flow equations using a derivative expansion of the scale-dependent effective action to second order and show that they reproduce the flow equations of the sine-Gordon model (obtained by integrating out the field $\vartheta$ from the outset) derived within the same approximation. Only with the scale-dependent (flowing) reparametrization of the phase field $\vartheta$ do we obtain the standard phenomenology of the Luttinger liquid (when the periodic potential is sufficiently weak so as to avoid the Mott-insulating phase) characterized by two low-energy parameters, the velocity of the sound mode and the renormalized Luttinger parameter.

  2 citations

• Exceptional points and pseudo-Hermiticity in real potential scattering

  Farhang Loran, Ali Mostafazadeh

  SciPost Phys. 12, 109 (2022) · published 28 March 2022 | Toggle abstract · pdf

  We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials. The transfer matrix for these potentials is related to the time-evolution operator for an associated pseudo-Hermitian Hamiltonian operator $\widehat{\boldsymbol{H}}$ which develops an exceptional point for a discrete set of incident wavenumbers. We use the spectral properties of this operator to determine the transfer matrix of these potentials and solve their scattering problem. We apply our general results to explore the scattering of waves by a waveguide of finite length in two dimensions, where the source of the incident wave and the detectors measuring the scattered wave are positioned at spatial infinities while the interior of the waveguide, which is filled with an inactive material, forms a finite rectangular region of the space. The study of this model allows us to elucidate the physical meaning and implications of the presence of the real and complex eigenvalues of $\widehat{\boldsymbol{H}}$ and its exceptional points. Our results reveal the relevance of the concepts of pseudo-Hermitian operator and exceptional point in the standard quantum mechanics of closed systems where the potentials are required to be real.

  1 citation