Publications

Order by: publication date number of citations

• Excitations and ergodicity of critical quantum spin chains from non-equilibrium classical dynamics

  Stéphane Vinet, Gabriel Longpré, William Witczak-Krempa

  SciPost Phys. Core 5, 035 (2022) · published 7 July 2022 | Toggle abstract · pdf

  We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising couplings normalized by the bath's temperature. We give its exact ground states. Proceeding with uniform couplings, we study the one- and two-magnon excitations. Solutions for the latter are derived via a Bethe Ansatz scheme. In the antiferromagnetic regime, the two-magnon branch states show intricate behavior, especially regarding their hybridization with the continuum. We find that that the gapless chain hosts multiple dynamics at low energy as seen through the presence of multiple dynamical critical exponents. Finally, we analyze the full energy level spacing distribution as a function of the Ising coupling. We conclude that the system is non-integrable for generic parameters, or equivalently, that the corresponding non-equilibrium classical dynamics are ergodic.

  1 citation

• A constructive theory of the numerically accessible many-body localized to thermal crossover

  Philip J D Crowley, Anushya Chandran

  SciPost Phys. 12, 201 (2022) · published 24 June 2022 | Toggle abstract · pdf

  The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent $\nu=1$, exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent $1/\omega$ dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes $L$ which are smaller than a \emph{resonance length} $\lambda$. For $L \gg \sqrt{\lambda}$ (in lattice units), resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [Suntajs et al 2019, Sels & Polkovnikov 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

  46 citations

• On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

  Christian Hagendorf, Gilles Parez

  SciPost Phys. 12, 199 (2022) · published 24 June 2022 | Toggle abstract · pdf

  The open XXZ spin chain with the anisotropy $\Delta=-\frac12$ and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain's ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state's logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.

  2 citations

• Optomechanical damping as the origin of sideband asymmetry

  João D. P. Machado, Yaroslav M. Blanter

  SciPost Phys. Core 5, 034 (2022) · published 23 June 2022 | Toggle abstract · pdf

  Sideband asymmetry in cavity optomechanics has been explained by particle creation and annihilation processes, which bestow an amplitude proportional to 'n+1' and 'n' excitations to each of the respective sidebands. We discuss the issues with this as well as other interpretations, such as quantum backaction and noise interference, and show that the asymmetry is due to the optomechanical damping caused by the probe and the cooling lasers instead.

  1 citation

• Rényi entropies and negative central charges in non-Hermitian quantum systems

  Yi-Ting Tu, Yu-Chin Tzeng, Po-Yao Chang

  SciPost Phys. 12, 194 (2022) · published 13 June 2022 | Toggle abstract · pdf

  Quantum entanglement is one essential element to characterize many-body quantum systems. However, the entanglement measures are mostly discussed in Hermitian systems. Here, we propose a natural extension of entanglement and R\'enyi entropies to non-Hermitian quantum systems. There have been other proposals for the computation of these quantities, which are distinct from what is proposed in the current paper. We demonstrate the proposed entanglement quantities which are referred to as generic entanglement and R\'enyi entropies. These quantities capture the desired entanglement properties in non-Hermitian critical systems, where the low-energy properties are governed by the non-unitary conformal field theories (CFTs). We find excellent agreement between the numerical extrapolation of the negative central charges from the generic entanglement/R\'enyi entropy and the non-unitary CFT prediction. Furthermore, we apply the generic entanglement/R\'enyi entropy to symmetry-protected topological phases with non-Hermitian perturbations. We find the generic $n$-th R\'enyi entropy captures the expected entanglement property, whereas the traditional R\'enyi entropy can exhibit unnatural singularities due to its improper definition.

  18 citations

• Shallow trimers of two identical fermions and one particle in resonant regimes

  Pascal Naidon, Ludovic Pricoupenko, Christiane Schmickler

  SciPost Phys. 12, 185 (2022) · published 7 June 2022 | Toggle abstract · pdf

  We consider two identical fermions interacting in the p-wave channel. Each fermion also interacts with another particle in the vicinity of an s-wave resonance. We find that in addition to the Kartavtsev-Malykh universal trimer states resulting from the s-wave particle-fermion interaction, the fermion-fermion p-wave interaction induces one or two shallow trimers in a large domain of the control parameters, including a borromean regime where the ground-state trimer exists in the absence of dimers at any mass ratio between the fermions and the particle. A generic picture of the trimer spectrum emerges from this work in terms of the low-energy parameters of the interactions.

  4 citations

• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field

  Natalia Chepiga

  SciPost Phys. Core 5, 031 (2022) · published 30 May 2022 | Toggle abstract · pdf

  By computing the low-lying energy excitation spectra with the density matrix renormalization group algorithm we show that boundaries polarized in the direction of the transverse field lead to scale-invariant conformal towers of states at the critical point of the quantum four-state Potts model - a special symmetric case of the Ashkin-Teller model. Furthermore, by direct comparison of the excitation spectra we phenomenologically establish the duality between the transverse-polarized and three-state-mixed boundary conditions at the four-state Potts critical point. Finally, for completeness, we verify that in the quantum three-state Potts model the "new" boundary conditions dual to the mixed ones can be realized by polarizing edge spins along the transverse field.

  3 citations

• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations

  Oleksandr Gamayun, Oleg Lychkovskiy

  SciPost Phys. 12, 175 (2022) · published 25 May 2022 | Toggle abstract · pdf

  The Kitaev model on the honeycomb lattice, while being integrable via the spin-fermion mapping, has generally resisted an analytical treatment of the far-from-equilibrium dynamics due to the extensive number of relevant configurations of conserved charges. Here we study a close proxy of this model, the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. Instead of relying on the spin-fermion mapping, we take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. The simplest operator in this subset corresponds to the energy contribution of a single bond direction. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant (or staggered-translation-invariant) initial state with arbitrary initial (staggered) polarization.

  1 citation

• New directions in the search for dark matter

  Surjeet Rajendran

  SciPost Phys. Lect. Notes 56 (2022) · published 23 May 2022 | Toggle abstract · pdf

  The identification of the nature of dark matter is one of the most important problems confronting particle physics. Current observational constraints permit the mass of the dark matter to range from $\sim 10^{-22}$ eV - $10^{48}$ GeV. Given the weak nature of these bounds and the ease with which dark matter models can be constructed, it is clear that the problem can only be solved experimentally. In these lectures, I discuss methods to experimentally probe a wide range of dark matter candidates.

  3 citations

• Probabilistically violating the first law of thermodynamics in a quantum heat engine

  Timo Kerremans, Peter Samuelsson, Patrick P. Potts

  SciPost Phys. 12, 168 (2022) · published 20 May 2022 | Toggle abstract · pdf

  Fluctuations of thermodynamic observables, such as heat and work, contain relevant information on the underlying physical process. These fluctuations are however not taken into account in the traditional laws of thermodynamics. While the second law is extended to fluctuating systems by the celebrated fluctuation theorems, the first law is generally believed to hold even in the presence of fluctuations. Here we show that in the presence of quantum fluctuations, also the first law of thermodynamics may break down. This happens because quantum mechanics imposes constraints on the knowledge of heat and work. To illustrate our results, we provide a detailed case-study of work and heat fluctuations in a quantum heat engine based on a circuit QED architecture. We find probabilistic violations of the first law and show that they are closely connected to quantum signatures related to negative quasi-probabilities. Our results imply that in the presence of quantum fluctuations, the first law of thermodynamics may not be applicable to individual experimental runs.

  9 citations