Publications

Order by: publication date number of citations

• QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems. Part II: bosons, fermions and higher spins

  Phillip Weinberg, Marin Bukov

  SciPost Phys. 7, 020 (2019) · published 9 August 2019 | Toggle abstract · pdf

  We present a major update to QuSpin, SciPostPhys.2.1.003 -- an open-source Python package for exact diagonalization and quantum dynamics of arbitrary boson, fermion and spin many-body systems, supporting the use of various (user-defined) symmetries in one and higher dimension and (imaginary) time evolution following a user-specified driving protocol. We explain how to use the new features of QuSpin using seven detailed examples of various complexity: (i) the transverse-field Ising chain and the Jordan-Wigner transformation, (ii) free particle systems: the Su-Schrieffer-Heeger (SSH) model, (iii) the many-body localized 1D Fermi-Hubbard model, (iv) the Bose-Hubbard model in a ladder geometry, (v) nonlinear (imaginary) time evolution and the Gross-Pitaevskii equation on a 1D lattice, (vi) integrability breaking and thermalizing dynamics in the translationally-invariant 2D transverse-field Ising model, and (vii) out-of-equilibrium Bose-Fermi mixtures. This easily accessible and user-friendly package can serve various purposes, including educational and cutting-edge experimental and theoretical research. The complete package documentation is available under http://weinbe58.github.io/QuSpin/index.html.

  176 citations

• Geometry of variational methods: dynamics of closed quantum systems

  Lucas Hackl, Tommaso Guaita, Tao Shi, Jutho Haegeman, Eugene Demler, J. Ignacio Cirac

  SciPost Phys. 9, 048 (2020) · published 8 October 2020 | Toggle abstract · pdf

  We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: K\"ahler and non-K\"ahler. Traditional variational methods typically require the variational family to be a K\"ahler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-K\"ahler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

  51 citations

• Symmetry-resolved dynamical purification in synthetic quantum matter

  Vittorio Vitale, Andreas Elben, Richard Kueng, Antoine Neven, Jose Carrasco, Barbara Kraus, Peter Zoller, Pasquale Calabrese, Benoit Vermersch, Marcello Dalmonte

  SciPost Phys. 12, 106 (2022) · published 25 March 2022 | Toggle abstract · pdf

  When a quantum system initialized in a product state is subjected to either coherent or incoherent dynamics, the entropy of any of its connected partitions generically increases as a function of time, signalling the inevitable spreading of (quantum) information throughout the system. Here, we show that, in the presence of continuous symmetries and under ubiquitous experimental conditions, symmetry-resolved information spreading is inhibited due to the competition of coherent and incoherent dynamics: in given quantum number sectors, entropy decreases as a function of time, signalling dynamical purification. Such dynamical purification bridges between two distinct short and intermediate time regimes, characterized by a log-volume and log-area entropy law, respectively. It is generic to symmetric quantum evolution, and as such occurs for different partition geometry and topology, and classes of (local) Liouville dynamics. We then develop a protocol to measure symmetry-resolved entropies and negativities in synthetic quantum systems based on the random unitary toolbox, and demonstrate the generality of dynamical purification using experimental data from trapped ion experiments [Brydges et al., Science 364, 260 (2019)]. Our work shows that symmetry plays a key role as a magnifying glass to characterize many-body dynamics in open quantum systems, and, in particular, in noisy-intermediate scale quantum devices.

  50 citations

• Beyond Lee-Huang-Yang description of self-bound Bose mixtures

  Miki Ota, Grigori E. Astrakharchik

  SciPost Phys. 9, 020 (2020) · published 18 August 2020 | Toggle abstract · pdf

  We investigate the properties of self-bound ultradilute Bose-Bose mixtures, beyond the Lee-Huang-Yang description. Our approach is based on the determination of the beyond mean-field corrections to the phonon modes of the mixture in a self-consistent way and calculation of the associated equation of state. The newly obtained ground state energies show excellent agreement with recent quantum Monte Carlo calculations, providing a simple and accurate description of the self-bound mixtures with contact type interaction. We further show numerical results for the equilibrium properties of the finite size droplet, by adjusting the Gross-Pitaevskii equation. Our analysis is extended to the one-dimensional mixtures where an excellent agreement with quantum Monte Carlo predictions is found for the equilibrium densities. Finally, we discuss the effects of temperature on the stability of the liquid phase.

  47 citations

• Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems

  Maximilian Kiefer-Emmanouilidis, Razmik Unanyan, Jesko Sirker, Michael Fleischhauer

  SciPost Phys. 8, 083 (2020) · published 3 June 2020 | Toggle abstract · pdf

  Entanglement in a pure state of a many-body system can be characterized by the R\'enyi entropies $S^{(\alpha)}=\ln\textrm{tr}(\rho^\alpha)/(1-\alpha)$ of the reduced density matrix $\rho$ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, $\ln S^{(2)}$ can be tightly bound---from above and below---by the much easier accessible R\'enyi number entropy $S^{(2)}_N=-\ln \sum_n p^2(n)$ which is a function of the probability distribution $p(n)$ of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth---albeit logarithmically slower---of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal disorder.

  41 citations

• Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium

  Jacopo De Nardis, Miłosz Panfil

  SciPost Phys. 1, 015 (2016) · published 30 December 2016 | Toggle abstract · pdf

  We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed balance relation valid for any equilibrium state.

  40 citations

• The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases

  Yannis Brun, Jérôme Dubail

  SciPost Phys. 4, 037 (2018) · published 25 June 2018 | Toggle abstract · pdf

  Motivated by the calculation of correlation functions in inhomogeneous one-dimensional (1d) quantum systems, the 2d Inhomogeneous Gaussian Free Field (IGFF) is studied and solved. The IGFF is defined in a domain $\Omega \subset \mathbb{R}^2$ equipped with a conformal class of metrics $[{\rm g}]$ and with a real positive coupling constant $K: \Omega \rightarrow \mathbb{R}_{>0}$ by the action $\mathcal{S}[h] = \frac{1}{8\pi } \int_\Omega \frac{\sqrt{{\rm g}} d^2 {\rm x}}{K({\rm x})} \, {\rm g}^{i j} (\partial_i h)(\partial_j h)$. All correlations functions of the IGFF are expressible in terms of the Green's functions of generalized Poisson operators that are familiar from 2d electrostatics in media with spatially varying dielectric constants. This formalism is then applied to the study of ground state correlations of the Lieb-Liniger gas trapped in an external potential $V(x)$. Relations with previous works on inhomogeneous Luttinger liquids are discussed. The main innovation here is in the identification of local observables $\hat{O} (x)$ in the microscopic model with their field theory counterparts $\partial_x h, e^{i h(x)}, e^{-i h(x)}$, etc., which involve non-universal coefficients that themselves depend on position --- a fact that, to the best of our knowledge, was overlooked in previous works on correlation functions of inhomogeneous Luttinger liquids ---, and that can be calculated thanks to Bethe Ansatz form factors formulae available for the homogeneous Lieb-Liniger model. Combining those position-dependent coefficients with the correlation functions of the IGFF, ground state correlation functions of the trapped gas are obtained. Numerical checks from DMRG are provided for density-density correlations and for the one-particle density matrix, showing excellent agreement.

  40 citations

• Emergence of PT-symmetry breaking in open quantum systems

  Julian Huber, Peter Kirton, Stefan Rotter, Peter Rabl

  SciPost Phys. 9, 052 (2020) · published 19 October 2020 | Toggle abstract · pdf

  The effect of PT-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. Here we generalize the definition of PT symmetry to finite-dimensional open quantum systems, which are described by a Markovian master equation. Specifically, we show that the invariance of this master equation under a certain symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected PT-symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe PT-symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.

  36 citations

• Why are fractional charges of orientifolds compatible with Dirac quantization?

  Yuji Tachikawa, Kazuya Yonekura

  SciPost Phys. 7, 058 (2019) · published 1 November 2019 | Toggle abstract · pdf

  Orientifold $p$-planes with $p\le4$ have fractional D$p$-charges, and therefore appear inconsistent with Dirac quantization with respect to D$(6-p)$-branes. We explain in detail how this issue is resolved by taking into account the anomaly of the worldvolume fermions using the $\eta$ invariants. We also point out relationships to the classification of interacting fermionic symmetry protected topological phases. In an appendix, we point out that the duality group of type IIB string theory is the pin+ version of the double cover of $GL(2,\mathbb{Z})$.

  35 citations

• Anomalous mobility edges in one-dimensional quasiperiodic models

  Tong Liu, Xu Xia, Stefano Longhi, Laurent Sanchez-Palencia

  SciPost Phys. 12, 027 (2022) · published 18 January 2022 | Toggle abstract · pdf

  Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate bands of localized states from bands of critical states in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite band of critical states. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.

  34 citations