Order from disorder phenomena in BaCoS2

Lenz B., At T N ≃ 300K the layered insulator BaCoS2 transitions to a columnar antiferromagnet that signals non-negligible magnetic frustration despite the relatively high T N, all the more surprising given its quasi two-dimensional structure. Here, we show, by combining ab initio and model calculations, that the magnetic transition is an order-from-disorder phenomenon, which not only drives the columnar magnetic order, but also the inter-layer coherence responsible for the finite Néel transition temperature. This uncommon ordering mechanism, actively contributed by orbital degrees of freedom, hints at an abundance of low energy excitations above and across the Néel transition, in agreement with experimental evidence.

Renormalization group analysis of the Anderson model on random regular graphs

Vanoni C., Altshuler B.L., Kravtsov V.E., We present a renormalization group (RG) analysis of the problem of Anderson localization on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The RG equations necessarily involve two parameters (one being the changing connectivity of subtrees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the nonmonotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence. Our theory provides a simple and coherent explanation for the unusual scaling behavior observed in numerical data of the Anderson model on RRG and of many-body localization.

Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model

Fontana P., We investigate the band structure of the three-dimensional Hofstadter model on cubic lattices, with an isotropic magnetic field oriented along the diagonal of the cube with flux φ=2πm/n, where m,n are coprime integers. Using reduced exact diagonalization in momentum space, we show that, at fixed m, there exists an integer n(m) associated with a specific value of the magnetic flux, that we denote by φc(m)2πm/n(m), separating two different regimes. The first one, for fluxes φ<φc(m), is characterized by complete band overlaps, while the second one, for φ>φc(m), features isolated band-touching points in the density of states and Weyl points between the mth and the (m+1)-th bands. In the Hasegawa gauge, the minimum of the (m+1)-th band abruptly moves at the critical flux φc(m) from kz=0 to kz=π. We then argue that the limit for large m of φc(m) exists and it is finite: limm→∞φc(m)φc. Our estimate is φc/2π=0.1296(1). Based on the values of n(m) determined for integers m≤60, we propose a mathematical conjecture for the form of φc(m) to be used in the large-m limit. The asymptotic critical flux obtained using this conjecture is φc(conj)/2π=7/54.

Nonstabilizerness versus entanglement in matrix product states

Frau M., Tarabunga P.S., In this paper, we investigate the relationship between entanglement and nonstabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the nonstabilizer analog of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains. Our results indicate that obtaining converged results for nonstabilizerness is typically considerably easier than entanglement. For full state magic at critical points and at sufficiently large volumes, we observe convergence with 1/χ2, with χ being the MPS bond dimension. At small volumes, magic saturation is so quick that, within error bars, we cannot appreciate any finite-χ correction. Mutual magic also shows a fast convergence with bond dimension, whose specific functional form is however hindered by sampling errors. As a byproduct of our study, we show how Pauli-Markov chains (originally formulated to evaluate magic) resets the state of the art in terms of computing mutual information for MPS. We illustrate this last fact by verifying the logarithmic increase of mutual information between connected partitions at critical points. By comparing mutual information and mutual magic, we observe that, for connected partitions, the latter is typically scaling much slower - if at all - with the partition size, while for disconnected partitions, both are constant in size.

Principal deuterium Hugoniot via quantum Monte Carlo and Δ -learning

Tenti G., Nakano K., Tirelli A., We present a study of the principal deuterium Hugoniot for pressures up to 150 GPa, using machine learning potentials (MLPs) trained with quantum Monte Carlo (QMC) energies, forces, and pressures. In particular, we adopted a recently proposed workflow based on the combination of Gaussian kernel regression and Δ-learning. By fully taking advantage of this method, we explicitly considered finite-temperature electrons in the dynamics, whose effects are highly relevant for temperatures above 10 kK. The Hugoniot curve obtained by our MLPs shows a good agreement with the most recent experiments, particularly in the region below 60 GPa. At larger pressures, our Hugoniot curve is slightly more compressible than the one yielded by experiments, whose uncertainties generally increase, however, with pressure. Our work demonstrates that QMC can be successfully combined with Δ-learning to deploy reliable MLPs for complex extended systems across different thermodynamic conditions, by keeping the QMC precision at the computational cost of a mean-field calculation.

Unveiling the Stabilizer Group of a Matrix Product State

Lami G., We present a novel classical algorithm designed to learn the stabilizer group - namely, the group of Pauli strings for which a state is a ±1 eigenvector - of a given matrix product state (MPS). The algorithm is based on a clever and theoretically grounded biased sampling in the Pauli (or Bell) basis. Its output is a set of independent stabilizer generators whose total number is directly associated with the stabilizer nullity, notably a well-established nonstabilizer monotone. We benchmark our method on T-doped states randomly scrambled via Clifford unitary dynamics, demonstrating very accurate estimates up to highly entangled MPS with bond dimension χ∼103. Our method, thanks to a very favorable scaling O(χ3), represents the first effective approach to obtain a genuine magic monotone for MPS, enabling systematic investigations of quantum many-body physics out of equilibrium.

Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems

Rylands C., Klobas K., Ares F., The highly complicated nature of far from equilibrium systems can lead to a complete breakdown of the physical intuition developed in equilibrium. A famous example of this is the Mpemba effect, which states that nonequilibrium states may relax faster when they are further from equilibrium or, put another way, hot water can freeze faster than warm water. Despite possessing a storied history, the precise criteria and mechanisms underpinning this phenomenon are still not known. Here, we study a quantum version of the Mpemba effect that takes place in closed many-body systems with a U(1) conserved charge: in certain cases a more asymmetric initial configuration relaxes and restores the symmetry faster than a more symmetric one. In contrast to the classical case, we establish the criteria for this to occur in arbitrary integrable quantum systems using the recently introduced entanglement asymmetry. We describe the quantum Mpemba effect in such systems and relate the properties of the initial state, specifically its charge fluctuations, to the criteria for its occurrence. These criteria are expounded using exact analytic and numerical techniques in several examples, a free fermion model, the Rule 54 cellular automaton, and the Lieb-Liniger model.

Observing the Quantum Mpemba Effect in Quantum Simulations

Joshi L.K., Franke J., Rath A., Ares F., Murciano S., Kranzl F., Blatt R., Zoller P., Vermersch B., The nonequilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this Letter, we experimentally investigate one of the most puzzling of these phenomena - the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and postprocessed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.

Nonstabilizerness via Matrix Product States in the Pauli Basis

Tarabunga P.S., Tirrito E., Bañuls M.C., Nonstabilizerness, also known as "magic,"stands as a crucial resource for achieving a potential advantage in quantum computing. Its connection to many-body physical phenomena is poorly understood at present, mostly due to a lack of practical methods to compute it at large scales. We present a novel approach for the evaluation of nonstabilizerness within the framework of matrix product states (MPSs), based on expressing the MPS directly in the Pauli basis. Our framework provides a powerful tool for efficiently calculating various measures of nonstabilizerness, including stabilizer Rényi entropies, stabilizer nullity, and Bell magic, and enables the learning of the stabilizer group of an MPS. We showcase the efficacy and versatility of our method in the ground states of Ising and XXZ spin chains, as well as in circuits dynamics that has recently been realized in Rydberg atom arrays, where we provide concrete benchmarks for future experiments on logical qubits up to twice the sizes already realized.

Holographic thermal entropy from geodesic bit threads

Caggioli S., Gentile F., Seminara D., The holographic bit threads are an insightful tool to investigate the holographic entanglement entropy and other quantities related to the bipartite entanglement in AdS/CFT. We mainly explore the geodesic bit threads in various static backgrounds, for the bipartitions characterized by either a sphere or an infinite strip. In pure AdS and for the sphere, the geodesic bit threads provide a gravitational dual of the map implementing the geometric action of the modular conjugation in the dual CFT. In Schwarzschild AdS black brane and for the sphere, our numerical analysis shows that the flux of the geodesic bit threads through the horizon gives the holographic thermal entropy of the sphere. This feature is not observed when the subsystem is an infinite strip, whenever we can construct the corresponding bit threads. The bit threads are also determined by the global structure of the gravitational background; indeed, for instance, we show that the geodesic bit threads of an arc in the BTZ black hole cannot be constructed.

Optimal control of a quantum sensor: A fast algorithm based on an analytic solution

Hernández-Gómez S., Balducci F., Fasiolo G., Cappellaro P., Fabbri N., Quantum sensors can show unprecedented sensitivities, provided they are controlled in a very specific, optimal way. Here, we consider a spin sensor of time-varying fields in the presence of dephasing noise, and we show that the problem of finding the pulsed control field that optimizes the sensitivity (i.e., the smallest detectable signal) can be mapped to the determination of the ground state of a spin chain. We find an approximate but analytic solution of this problem, which provides a lower bound for the sensitivity and a pulsed control very close to optimal, which we further use as initial guess for realizing a fast simulated annealing algorithm. We experimentally demonstrate the sensitivity improvement for a spin-qubit magnetometer based on a nitrogen-vacancy center in diamond.

Entanglement Hamiltonian in the non-Hermitian SSH model

Rottoli F., Fossati M., Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature linear in the lattice index. At the critical point, we identify a new imaginary chemical potential term absent in unitary models. This operator is responsible for the negative entanglement entropy observed in the non-Hermitian SSH chain at criticality.

X-Ray Emission from Atomic Systems Can Distinguish between Prevailing Dynamical Wave-Function Collapse Models

Piscicchia K., Donadi S., Manti S., In this work the spontaneous electromagnetic radiation from atomic systems, induced by dynamical wave-function collapse, is investigated in the x-ray domain. Strong departures are evidenced with respect to the simple cases considered until now in the literature, in which the emission is either perfectly coherent (protons in the same nuclei) or incoherent (electrons). In this low-energy regime the spontaneous radiation rate strongly depends on the atomic species under investigation and, for the first time, is found to depend on the specific collapse model.

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Nakano K., Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

Noninterferometric rotational test of the continuous spontaneous localization model: Enhancement of the collapse noise through shape optimization

Altamura D.G.A., Carlesso M., Donadi S., The continuous spontaneous localization (CSL) model is the most studied among collapse models, which describes the breakdown of the superposition principle for macroscopic systems. Here, we derive an upper bound on the parameters of the model by applying it to the rotational noise measured in a recent short-distance gravity experiment [Lee, Phys. Rev. Lett. 124, 101101 (2020)0031-900710.1103/PhysRevLett.124.101101]. Specifically, considering the noise affecting the rotational motion, we found that despite being a tabletop experiment the bound is only one order of magnitude weaker than that from LIGO for the relevant values of the collapse parameter. Further, we analyze possible ways to optimize the shape of the test mass to enhance the collapse noise by several orders of magnitude and eventually derive stronger bounds that can address the unexplored region of the CSL parameters space.

Terrestrial very-long-baseline atom interferometry: Workshop summary

Abend S., Allard B., Alonso I., Antoniadis J., Araujo H., Arduini G., Arnold A.S., Asano T., Augst N., Badurina L., Balaz A., Banks H., Barone M., Barsanti M., This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more kilometer–scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions.

Changing the order of a dynamical phase transition through fluctuations in a quantum p-spin model

Correale L., We study the non-equilibrium phase diagram of a fully-connected Ising p-spin model, for generic p > 2, and investigate its robustness with respect to the inclusion of spin-wave fluctuations, resulting from a ferromagnetic, short-range spin interaction. In particular, we investigate the dynamics of the mean-field model after a quantum quench: we observe a new dynamical phase transition which is either first or second order depending on the even or odd parity of p, in stark contrast with its thermal counterpart which is first order for all p. The dynamical phase diagram is qualitatively modified by the fluctuations introduced by a short-range interaction which drive the system always towards various prethermal paramagnetic phases determined by the strength of time dependent fluctuations of the magnetization.

Dynamics of charge fluctuations from asymmetric initial states

Bertini B., Klobas K., Conserved-charge densities are very special observables in quantum many-body systems as, by construction, they encode information about the dynamics. Therefore, their evolution is expected to be of much simpler interpretation than that of generic observables and to return universal information on the state of the system at any given time. Here, we study the dynamics of the fluctuations of conserved U(1) charges in systems that are prepared in charge-asymmetric initial states. We characterize the charge fluctuations in a given subsystem using the full-counting statistics of the truncated charge and the quantum entanglement between the subsystem and the rest resolved to the symmetry sectors of the charge. We show that, even though the initial states considered are homogeneous in space, the charge fluctuations generate an effective inhomogeneity due to the charge-asymmetric nature of the initial states. We use this observation to map the problem into that of charge fluctuations on inhomogeneous, charge-symmetric states and treat it using a recently developed space-time duality approach. Specializing the treatment to interacting integrable systems we combine the space-time duality approach with generalized hydrodynamics to find explicit predictions.

Floquet time crystals as quantum sensors of ac fields

Iemini F., The long-range spatial and temporal ordering displayed by discrete time crystals, can become advantageous properties when used for sensing extremely weak signals. Here, we investigate their performance as quantum sensors of weak ac fields and demonstrate, using the quantum Fisher information measure, that they can overcome the shot-noise limit while allowing long interrogation times. In such systems, collective interactions stabilize their dynamics against noise, making them robust enough to protocol imperfections.

Entanglement entropies of an interval for the massless scalar field in the presence of a boundary

Estienne B., Ikhlef Y., Rotaru A., We study the entanglement entropies of an interval for the massless compact boson either on the half line or on a finite segment, when either Dirichlet or Neumann boundary conditions are imposed. In these boundary conformal field theory models, the method of the branch point twist fields is employed to obtain analytic expressions for the two-point functions of twist operators. In the decompactification regime, these analytic predictions in the continuum are compared with the lattice numerical results in massless harmonic chains for the corresponding entanglement entropies, finding good agreement. The application of these analytic results in the context of quantum quenches is also discussed.