Publications

Order by: publication date number of citations

• Elaborating the phase diagram of spin-1 anyonic chains

  Eric Vernier, Jesper Lykke Jacobsen, Hubert Saleur

  SciPost Phys. 2, 004 (2017) · published 21 February 2017 | Toggle abstract · pdf

  We revisit the phase diagram of spin-1 $su(2)_k$ anyonic chains, originally studied by Gils {\it et. al.} [Phys. Rev. B, {\bf 87} (23) (2013)]. These chains possess several integrable points, which were overlooked (or only briefly considered) so far. Exploiting integrability through a combination of algebraic techniques and exact Bethe ansatz results, we establish in particular the presence of new first order phase transitions, a new critical point described by a $Z_k$ parafermionic CFT, and of even more phases than originally conjectured. Our results leave room for yet more progress in the understanding of spin-1 anyonic chains.

  7 citations

• QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems part I: spin chains

  Phillip Weinberg, Marin Bukov

  SciPost Phys. 2, 003 (2017) · published 13 February 2017 | Toggle abstract · pdf

  We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon) chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary) time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet) systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i) Standard exact diagonalisation of XXZ chain (ii) adiabatic ramping of parameters in the many-body localised XXZ model, (iii) heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv) quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.

  350 citations

• Universal front propagation in the quantum Ising chain with domain-wall initial states

  Viktor Eisler, Florian Maislinger, Hans Gerd Evertz

  SciPost Phys. 1, 014 (2016) · published 30 December 2016 | Toggle abstract · pdf

  We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.

  51 citations

• Detecting a many-body mobility edge with quantum quenches

  Piero Naldesi, Elisa Ercolessi, Tommaso Roscilde

  SciPost Phys. 1, 010 (2016) · published 27 October 2016 | Toggle abstract · pdf

  The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to "localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

  60 citations

• A conformal bootstrap approach to critical percolation in two dimensions

  Marco Picco, Sylvain Ribault, Raoul Santachiara

  SciPost Phys. 1, 009 (2016) · published 27 October 2016 | Toggle abstract · pdf

  We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.

  44 citations

• Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra

  T. Scoquart, J. J. Seaward, S. G. Jackson, M. Olshanii

  SciPost Phys. 1, 005 (2016) · published 23 October 2016 | Toggle abstract · pdf

  The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line, related to the symmetry of a regular icosahedron: in two distinct limiting cases the system is constrained to a half-line. We repeat the program for a 600-cell, a four-dimensional generalization of the regular three-dimensional icosahedron.

  7 citations

• Quantum-optical magnets with competing short- and long-range interactions: Rydberg-dressed spin lattice in an optical cavity

  Jan Gelhausen, Michael Buchhold, Achim Rosch, Philipp Strack

  SciPost Phys. 1, 004 (2016) · published 23 October 2016 | Toggle abstract · pdf

  The fields of quantum simulation with cold atoms [1] and quantum optics [2] are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities [3,4] lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range -mediated by a quantized optical light field- were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms $N\rightarrow\infty$, (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice [5] coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice Master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field can coexist with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.

  23 citations

• Quantum quenches to the attractive one-dimensional Bose gas: exact results

  Lorenzo Piroli, Pasquale Calabrese, Fabian H. L. Essler

  SciPost Phys. 1, 001 (2016) · published 14 September 2016 | Toggle abstract · pdf

  We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function $g_2$.

  60 citations