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Crossed product algebras and generalized entropy for subregions

Shadi Ali Ahmad, Ro Jefferson

SciPost Phys. Core 7, 020 (2024) · published 10 April 2024 | · pdf

An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III$_{1}$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states. However, associated to the algebra is a modular group of automorphisms characterizing the local dynamics of degrees of freedom in the region, and the crossed product of the algebra with its modular group yields a type II$_∞$ factor, in which traces and hence von Neumann entropy can be well-defined. In this work, we generalize recent constructions of the crossed product algebra for the TFD to, in principle, arbitrary spacetime regions in arbitrary QFTs, formally paving the way to the study of entanglement entropy without UV divergences. In contrast to previous works, we emphasize that this construction is independent of gravity. In this sense, the crossed product construction represents a refinement of Haag's assignment of nets of observable algebras to spacetime regions by providing a natural construction of a type II factor. We present several concrete examples: a QFT in Rindler space, a CFT in an open ball of Minkowski space, and arbitrary boundary subregions in AdS/CFT. In the holographic setting, we provide a novel argument for why the bulk dual must be the entanglement wedge, and discuss the distinction arising from boundary modular flow between causal and entanglement wedges for excited states and disjoint regions.
Design constraints for Unruh-DeWitt quantum computers

Eric W. Aspling, John A. Marohn, Michael J. Lawler

SciPost Phys. Core 7, 019 (2024) · published 10 April 2024 | · pdf

The Unruh-DeWitt particle detector model has found success in demonstrating quantum information channels with non-zero channel capacity between qubits and quantum fields. These detector models provide the necessary framework for experimentally realizable Unruh-DeWitt quantum computers with near-perfect channel capacity. We propose spin-qubits with gate-controlled coupling to Luttinger liquids as a laboratory setting for Unruh-DeWitt detectors and explore general design constraints that underpin their feasibility in this and other settings. We present several experimental scenarios including graphene ribbons, edges states in the quantum spin Hall phase of HgTe quantum wells, and the recently discovered quantum anomalous Hall phase in transition metal dichalcogenides. Theoretically, through bosonization, we show that Unruh-DeWitt detectors can carry out quantum computations and identify when they can make perfect quantum communication channels between qubits via the Luttinger liquid. Our results point the way toward an all-to-all connected solid state quantum computer and the experimental study of quantum information in quantum fields via condensed matter physics.
Hidden symmetry of Bogoliubov de Gennes quasi-particle eigenstates and universal relations in flat band superconducting bipartite lattices

Georges Bouzerar, Maxime Thumin

SciPost Phys. Core 7, 018 (2024) · published 9 April 2024 | · pdf

Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T$_c$ materials. In FBs, pairings and superfluid weight scale linearly with the interaction parameter, such an unusual behaviour justifies and encourages strategies to promote FB engineering. Bipartite lattices (BLs) which naturally host FBs could be particularly interesting candidates. Within Bogoliubov de Gennes theory and in the framework of the attractive Hubbard model in BLs, a hidden symmetry of the quasi-particle eigenstates is revealed. As a consequence, we demonstrate universal relations for the pairings and the superfluid weight that are independent of the characteristics of the hopping term. Remarkably, it is shown that these general properties are insensitive to disorder as long as the bipartite character is protected.
Thermalization of long range Ising model in different dynamical regimes: A full counting statistics approach

Nishan Ranabhat, Mario Collura

SciPost Phys. Core 7, 017 (2024) · published 5 April 2024 | · pdf

We study the thermalization of the transverse field Ising chain with a power law decaying interaction $\sim 1/r^{\alpha}$ following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths $\alpha$, whereas thermalization occurs in the region with weak confinement.
Stochastic series expansion quantum Monte Carlo for Rydberg arrays

Ejaaz Merali, Isaac J. S. De Vlugt, Roger G. Melko

SciPost Phys. Core 7, 016 (2024) · published 5 April 2024 | · pdf

Arrays of Rydberg atoms are a powerful platform to realize strongly-interacting quantum many-body systems. A common Rydberg Hamiltonian is free of the sign problem, meaning that its equilibrium properties are amenable to efficient simulation by quantum Monte Carlo (QMC). In this paper, we develop a Stochastic Series Expansion QMC algorithm for Rydberg atoms interacting on arbitrary lattices. We describe a cluster update that allows for the efficient sampling and calculation of physical observables for typical experimental parameters, and show that the algorithm can reproduce experimental results on large Rydberg arrays in one and two dimensions.
Speed of sound in dense strong-interaction matter

Jens Braun, Andreas Geißel, Benedikt Schallmo

SciPost Phys. Core 7, 015 (2024) · published 5 April 2024 | · pdf

We study the speed of sound in strong-interaction matter at zero temperature and in density regimes which are expected to be governed by the presence of a color-superconducting gap. At (very) high densities, our analysis indicates that the speed of sound approaches its asymptotic value associated with the non-interacting quark gas from below, in agreement with first-principles studies which do not take the presence of a color-superconducting gap into account. Towards lower densities, however, the presence of a gap induces an increase of the speed of sound above its asymptotic value. Importantly, even if gap-induced corrections to the pressure may appear small, we find that derivatives of the gap with respect to the chemical potential can still be sizeable and lead to a qualitative change of the density dependence of the speed of sound. Taking into account constraints on the density dependence of the speed of sound at low densities, our general considerations suggest the existence of a maximum in the speed of sound. Interestingly, we also observe that specific properties of the gap can be related to characteristic properties of the speed of sound which are indirectly constrained by observations.
Abelian combinatorial gauge symmetry

Hongji Yu, Dmitry Green, Andrei E. Ruckenstein, Claudio Chamon

SciPost Phys. Core 7, 014 (2024) · published 26 March 2024 | · pdf

Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This paper is a generalization of the construction to any finite Abelian group. In addition to the general mathematical construction, we present a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians.
A general learning scheme for classical and quantum Ising machines

Ludwig Schmid, Enrico Zardini, Davide Pastorello

SciPost Phys. Core 7, 013 (2024) · published 14 March 2024 | · pdf

An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is based on the Ising structure and can be efficiently trained using gradient descent. We provide a mathematical characterization of the training process, which is based upon optimizing a loss function whose partial derivatives are not explicitly calculated but estimated by the Ising machine itself. Moreover, we present some experimental results on the training and execution of the proposed learning model. These results point out new possibilities offered by Ising machines for different learning tasks. In particular, in the quantum realm, the quantum resources are used for both the execution and the training of the model, providing a promising perspective in quantum machine learning.
Stochastic field dynamics in models of spontaneous unitarity violation

Lotte Mertens, Matthijs Wesseling, Jasper van Wezel

SciPost Phys. Core 7, 012 (2024) · published 13 March 2024 | · pdf

Objective collapse theories propose a solution to the quantum measurement problem by predicting deviations from Schrödinger's equation that can be tested experimentally. A class of objective theories based on spontaneous unitarity violation was recently introduced, in which the stochastic field required for obtaining Born's rule does not depend on the state of the system being measured. Here, we classify possible models for the stochastic field dynamics in theories of spontaneous unitarity violation. We show that for correlated stochastic dynamics, the field must be defined on a closed manifold. In two or more dimensions, it is then always possible to find stochastic dynamics yielding Born's rule, independent of the state being measured or the correlation time of the stochastic field. We show that the models defined this way are all isomorphic to the definition on a two-sphere, which we propose to be a minimal physical model for the stochastic field in models of spontaneous unitarity violation.
Measurement induced transitions in non-Markovian free fermion ladders

Mikheil Tsitsishvili, Dario Poletti, Marcello Dalmonte, Giuliano Chiriacò

SciPost Phys. Core 7, 011 (2024) · published 12 March 2024 | · pdf

Recently there has been an intense effort to understand measurement induced transitions, but we still lack a good understanding of non-Markovian effects on these phenomena. To that end, we consider two coupled chains of free fermions, one acting as the system of interest, and one as a bath. The bath chain is subject to Markovian measurements, resulting in an effective non-Markovian dissipative dynamics acting on the system chain which is still amenable to numerical studies in terms of quantum trajectories. Within this setting, we study the entanglement within the system chain, and use it to characterize the phase diagram depending on the ladder hopping parameters and on the measurement probability. For the case of pure state evolution, the system is in an area law phase when the internal hopping of the bath chain is small, while a non-area law phase appears when the dynamics of the bath is fast. The non-area law exhibits a logarithmic scaling of the entropy compatible with a conformal phase, but also displays linear corrections for the finite system sizes we can study. For the case of mixed state evolution, we instead observe regions with both area, and non-area scaling of the entanglement negativity. We quantify the non-Markovianity of the system chain dynamics and find that for the regimes of parameters we study, a stronger non-Markovianity is associated to a larger entanglement within the system.

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