Publications

Order by: publication date number of citations

• Quantum Gross-Pitaevskii Equation

  Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

  SciPost Phys. 3, 006 (2017) · published 28 July 2017 | Toggle abstract · pdf

  We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

  12 citations

• Perturbative and nonperturbative studies of CFTs with MN global symmetry

  Johan Henriksson, Andreas Stergiou

  SciPost Phys. 11, 015 (2021) · published 16 July 2021 | Toggle abstract · pdf

  Fixed points in three dimensions described by conformal field theories with $MN_{m,n}= O(m)^n\rtimes S_n$ global symmetry have extensive applications in critical phenomena. Associated experimental data for $m=n=2$ suggest the existence of two non-trivial fixed points, while the $\varepsilon$ expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters $m$ and $n$, with critical exponents in good agreement with experimental determinations in the $m=n=2$ case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters $m$ and $n$. We find that one family of kinks approaches a perturbative limit as $m$ increases, and using large spin perturbation theory we construct a large $m$ expansion that fits well with the numerical data. This new expansion, akin to the large $N$ expansion of critical $O(N)$ models, is compatible with the fixed point found in the $\varepsilon$ expansion. For the other family of kinks, we find that it persists only for $n=2$, where for large $m$ it approaches a non-perturbative limit with $\Delta_\phi\approx 0.75$. We investigate the spectrum in the case $MN_{100,2}$ and find consistency with expectations from the lightcone bootstrap.

  12 citations

• Comments on a state-operator correspondence for the torus

  Alexandre Belin, Jan de Boer, Jorrit Kruthoff

  SciPost Phys. 5, 060 (2018) · published 10 December 2018 | Toggle abstract · pdf

  We investigate the existence of a state-operator correspondence on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the Horowitz-Myers conjecture for the AdS soliton.

  12 citations

• Quantum bounds and fluctuation-dissipation relations

  Silvia Pappalardi, Laura Foini, Jorge Kurchan

  SciPost Phys. 12, 130 (2022) · published 14 April 2022 | Toggle abstract · pdf

  In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and derivation of quantum bounds on the transport coefficients or on the chaos rate. However, the physical meaning and the mechanism enforcing such bounds is still an open question. Here, we discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, we show that the quantum bound to chaos is a direct consequence of the KMS condition, as applied to a particular pair of two-time correlation and response functions. Encouraged by this, we describe how quantum fluctuation-dissipation relations act in general as a blurring of the time-dependence of correlations, which can imply bounds on their decay rates. Thinking in terms of fluctuation-dissipation opens a direct connection between bounds and other thermodynamic properties.

  12 citations

• Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition

  Se Kwon Kim, Suk Bum Chung

  SciPost Phys. 10, 068 (2021) · published 12 March 2021 | Toggle abstract · pdf

  Motivated by recent experimental progress in 2D magnetism, we theoretically study spin transport in 2D easy-plane magnets at finite temperatures across the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, by developing a duality mapping to the 2+1D electromagnetism with the full account of spin's finite lifetime. In particular, we find that the non-conservation of spin gives rise to a distinct signature across the BKT transition, with the spin current decaying with distance power-law (exponentially) below (above) the transition; this is detectable in the proposed experiment with NiPS$_3$ and CrCl$_3$.

  12 citations

• Branch point twist field form factors in the sine-Gordon model I: Breather fusion and entanglement dynamics

  Olalla A. Castro-Alvaredo, David X. Horvath

  SciPost Phys. 10, 132 (2021) · published 4 June 2021 | Toggle abstract · pdf

  The quantum sine-Gordon model is the simplest massive interacting integrable quantum field theory whose two-particle scattering matrix is generally non-diagonal. As such, it is a model that has been extensively studied, especially in the context of the bootstrap programme. In this paper we compute the form factors of a special local field known as the branch point twist field, whose correlation functions are building blocks for measures of entanglement. We consider the attractive regime where the theory posesses a particle spectrum consisting of a soliton, an antisoliton (of opposite $U(1)$ charges) and several (neutral) breathers. In the breather sector we exploit the fusion procedure to compute form factors of heavier breathers from those of lighter ones. We apply our results to the study of the entanglement dynamics after a small mass quench and for short times. We show that in the presence of two or more breathers the von Neumann and R\'enyi entropies display undamped oscillations in time, whose frequencies are proportional to the even breather masses and whose amplitudes are proportional to the breather's one-particle form factor.

  12 citations

• Counting D1-D5-P microstates in supergravity

  Daniel R. Mayerson, Masaki Shigemori

  SciPost Phys. 10, 018 (2021) · published 27 January 2021 | Toggle abstract · pdf

  We quantize the D1-D5-P microstate geometries known as superstrata directly in supergravity. We use Rychkov's consistency condition [hep-th/0512053] which was derived for the D1-D5 system; for superstrata, this condition turns out to be strong enough to fix the symplectic form uniquely. For the $(1,0,n)$ superstrata, we further confirm this quantization by a bona-fide explicit computation of the symplectic form using the semi-classical covariant quantization method in supergravity. We use the resulting quantizations to count the known supergravity superstrata states, finding agreement with previous countings that the number of these states grows parametrically smaller than those of the corresponding black hole.

  12 citations

• Time-evolution of local information: thermalization dynamics of local observables

  Thomas Klein Kvorning, Loïc Herviou, Jens H. Bardarson

  SciPost Phys. 13, 080 (2022) · published 4 October 2022 | Toggle abstract · pdf

  Quantum many-body dynamics generically results in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such decoupling of local degrees of freedom for the mixed field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we can motivate algorithms based on the intuition that information for statistical reasons flow from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.

  12 citations

• Circular Rosenzweig-Porter random matrix ensemble

  Wouter Buijsman, Yevgeny Bar Lev

  SciPost Phys. 12, 082 (2022) · published 3 March 2022 | Toggle abstract · pdf

  The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across the many-body localization transition in static systems. We propose a unitary (circular) analogue of this ensemble, which similarly captures the phenomenology of many-body localization in periodically driven (Floquet) systems. We define this ensemble as the outcome of a Dyson Brownian motion process. We show numerical evidence that this ensemble shares some key statistical properties with the Rosenzweig-Porter ensemble for both the eigenvalues and the eigenstates.

  12 citations

• QGOpt: Riemannian optimization for quantum technologies

  Ilia A. Luchnikov, Alexander Ryzhov, Sergey N. Filippov, Henni Ouerdane

  SciPost Phys. 10, 079 (2021) · published 30 March 2021 | Toggle abstract · pdf

  Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on the underlying Riemannian structure of quantum-mechanical constraints and permits application of standard gradient based optimization methods while preserving quantum mechanical constraints. Moreover, QGOpt is written on top of TensorFlow, which enables automatic differentiation to calculate necessary gradients for optimization. We show two application examples: quantum gate decomposition and quantum tomography.

  12 citations