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The behavior of the helicity modulus has been frequently employed to investigate the onset of the topological order characterizing the low-temperature phase of the two-dimensional XY model. We here present how the analysis based on the use of this key quantity can be applied to the study of the properties of coupled layers. To this aim, we first discuss how to extend the popular worm algorithm to a layered sample, and in particular to the evaluation of the longitudinal helicity, that we introduce taking care of the fact that the virtual twist representing the elastic deformation one applies to properly define the helicity modulus can act on a single layer or on all of them. We then apply the method to investigate the bilayer XY model, showing how the helicity modulus can be used to determine the phase diagram of the model as a function of temperature and interlayer coupling strength.

We study the effect of competing interactions on ensemble inequivalence. We consider a one-dimensional Ising model with ferromagnetic mean-field interactions and short-range nearest-neighbor (NN) and next-NN couplings which can be either ferromagnetic or antiferromagnetic. Despite the relative simplicity of the model, our calculations in the microcanonical ensemble reveal a rich phase diagram. The comparison with the corresponding phase diagram in the canonical ensemble shows the presence of phase transition points and lines which are different in the two ensembles. As an example, in a region of the phase diagram where the canonical ensemble shows a critical point and a critical end point, the microcanonical ensemble has an additional critical point and also a triple point. The regions of ensemble inequivalence typically occur at lower temperatures and at larger absolute values of the competing couplings. The presence of two free parameters in the model allows us to obtain a fourth-order critical point, which can be fully characterized by deriving its Landau normal form.

Energy exchange statistics between two bodies at different thermal equilibria obey the Jarzynski-Wójcik fluctuation theorem. The corresponding energy scale factor is the difference of the inverse temperatures associated to the bodies at equilibrium. In this work, we consider a dissipative quantum dynamics leading the quantum system towards a possibly nonthermal, asymptotic state. To generalize the Jarzynski-Wójcik theorem to nonthermal states, we identify a sufficient condition I for the existence of an energy scale factor η∗ that is unique, finite, and time independent, such that the characteristic function of the energy exchange distribution becomes identically equal to 1 for any time. This η∗ plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition I, showing that it amounts to an almost complete memory loss of the initial state. The robustness of our results against quantifiable deviations from the validity of I is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.

We investigate the dynamics of one-dimensional interacting bosons in an optical lattice after a sudden quench in the weakly interacting (Bose-Hubbard) and strongly interacting (sine-Gordon) regimes. While in a higher dimension, the Mott-superfluid phase transition is observed for weakly interacting bosons in deep lattices, in one dimension an instability is generated also for shallow lattices with a commensurate periodic potential pinning the atoms to the Mott state through a transition described by the sine-Gordon model. The present work aims at identifying the quench dynamics in both the Bose-Hubbard and sine-Gordon interaction regimes. We numerically exactly solve the time-dependent Schrödinger equation for a small number of atoms and obtain dynamical measures of several key quantities. We investigate the correlation dynamics of first and second order; both exhibit rich many-body features in the dynamics. We conclude that in both cases, dynamics exhibits collapse-revival phenomena, though with different timescales. We argue that the dynamical fragmentation is a convenient quantity to distinguish the dynamics especially near the pinning zone. To understand the relaxation process we measure the many-body information entropy. Bose-Hubbard dynamics clearly establishes the possible relaxation to the maximum entropy state. In contrast, the sine-Gordon dynamics is so fast that it does not exhibit any signature of relaxation in the present timescale of computation.

In this paper we show how to measure in the setting of digital quantum simulations the reflection and transmission amplitudes of the one-dimensional scattering of a particle with a short-ranged potential. The main feature of the protocol is the coupling between the particle and an ancillary spin-1/2 degree of freedom. This allows us to reconstruct tomographically the scattering amplitudes, which are in general complex numbers, from the readout of one qubit. Applications of our results are discussed.

Time-evolution of the Universe as described by the Friedmann equation can be coupled to equations of motion of matter fields. Quantum effects may be incorporated to improve these classical equations of motion by the renormalization group (RG) running of their couplings. Since temporal and thermal evolutions are linked to each other, astrophysical and cosmological treatments based on zero-temperature RG methods require the extension to finite-temperatures. We propose and explore a modification of the usual finite-temperature RG approach by relating the temperature parameter to the running RG scale as T≡kT=τk (in natural units), where kT is acting as a running cutoff for thermal fluctuations and the momentum k can be used for the quantum fluctuations. In this approach, the temperature of the expanding universe is related to the dimensionless quantity τ (and not to kT). We show that by this choice dimensionless RG flow equations have no explicit k-dependence, as it is convenient. We also discuss how this modified thermal RG is used to handle high-energy divergences of the RG running of the cosmological constant and to “solve the triviality” of the ϕ4 model by a thermal phase transition in terms of τ in d=4 Euclidean dimensions.

We numerically study the expansion dynamics of initially localized dipolar bosons in a homogeneous 1D optical lattice for different initial states. Comparison is made to interacting bosons with contact interaction. For shallow lattices, the expansion is unimodal and ballistic, while strong lattices suppress tunneling. However, for intermediate lattice depths, a strong interplay between dipolar interaction and lattice depth occurs. The expansion is found to be bimodal, the central cloud expansion can be distinguished from the outer halo structure. In the regime of strongly interactions dipolar bosons exhibit two time-scales, with an initial diffusion and then arrested transport in the long time, while strongly interacting bosons in the fermionized limit exhibit ballistic expansion. Our study highlights how different lattice depths and initial states can be manipulated to control tunneling dynamics.

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.

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.

We study the 1D antiferromagnetic spin-1 Heisenberg XXX model with external magnetic field B and single-ion anisotropy D on finite chains. We determine the nearest and non-nearest neighbor logarithmic entanglement LN. Our main result is the disappearance of LN both for nearest and non-nearest neighbor (next-nearest and next-next-nearest) sites at zero temperature and for low-temperature states. Such disappearance occurs at a critical value of B and D. The resulting phase diagram for the behavior of LN is discussed in the B−D plane, including a separating line – ending in a triple point – where the energy density is independent on the size. Finally, results for LN at finite temperature as a function of B and D are presented and commented.

We report on the experimental quantification of the contribution to non-equilibrium entropy production stemming from the quantum coherence content in the initial state of a qubit exposed to both coherent driving and dissipation. Our experimental demonstration builds on the exquisite experimental control of the spin state of a nitrogen-vacancy defect in diamond and is underpinned, theoretically, by the formulation of a generalized fluctuation theorem designed to track the effects of quantum coherence. Our results provide significant evidence of the possibility to pinpoint the genuinely quantum mechanical contributions to the thermodynamics of non-equilibrium quantum processes in an open quantum systems scenario.

We perform a numerical study of transport properties of a one-dimensional chain with couplings decaying as an inverse power r-(1+σ) of the intersite distance r and open boundary conditions, interacting with two heat reservoirs. Despite its simplicity, the model displays highly nontrivial features in the strong long-range regime -1<σ<0. At weak coupling with the reservoirs, the energy flux departs from the predictions of perturbative theory and displays anomalous superdiffusive scaling of the heat current with the chain size. We trace this behavior back to the transmission spectrum of the chain, which displays a self-similar structure with a characteristic σ-dependent fractal dimension.

We discuss under which conditions multipartite entanglement in mixed quantum states can be characterized only in terms of two-point connected correlation functions, as it is the case for pure states. In turn, the latter correlations are defined via a suitable combination of (disconnected) one- and two-point correlation functions. In contrast to the case of pure states, conditions to be satisfied turn out to be rather severe. However, we were able to identify some interesting cases, as when the point-independence is valid of the one-point correlations in each possible decomposition of the density matrix, or when the operators that enter in the correlations are (semi-)positive/negative defined.

"Strange"correlators provide a tool to detect topological phases arising in many-body models by computing the matrix elements of suitably defined two-point correlations between the states under investigation and trivial reference states. Their effectiveness depends on the choice of the adopted operators. In this paper, we give a systematic procedure for this choice, discussing the advantages of choosing operators using the bulk-boundary correspondence of the systems under scrutiny. Via the scaling exponents, we directly relate the algebraic decay of the strange correlators with the scaling dimensions of gapless edge modes operators. We begin our analysis with lattice models hosting symmetry-protected topological phases and we analyze the sums of the strange correlators, pointing out that integrating their moduli substantially reduces cancellations and finite-size effects. We also analyze instances of systems hosting intrinsic topological order, as well as strange correlators between states with different nontrivial topologies. Our results for both translational and nontranslational invariant cases, and in the presence of on-site disorder and long-range couplings, extend the validity of the strange correlator approach for the diagnosis of topological phases of matter and indicate a general procedure for their optimal choice.

In this review recent investigations are summarized of many-body quantum systems with long-range interactions, which are currently realized in Rydberg atom arrays, dipolar systems, trapped-ion setups, and cold atoms in cavities. In these experimental platforms parameters can be easily changed, and control of the range of the interaction has been achieved. The main aim of the review is to present and identify the common and mostly universal features induced by long-range interactions in the behavior of quantum many-body systems. Discussed are the case of strong nonlocal couplings, i.e., the nonadditive regime, and the one in which energy is extensive, but low-energy, long-wavelength properties are altered with respect to the short-range case. When possible, comparisons with the corresponding results for classical systems are presented. Finally, cases of competition with local effects are also reviewed.

Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.

We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a nonperturbative one tied to angular-momentum conservation, and a perturbative one. A comparison with other schemes for (2+1)-dimensional quantum link models present in the literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.

We experimentally study a gas of quantum degenerate Rb87 atoms throughout the full dimensional crossover, from a one-dimensional (1D) system exhibiting phase fluctuations consistent with 1D theory to a three-dimensional (3D) phase-coherent system, thereby smoothly interpolating between these distinct, well-understood regimes. Using a hybrid trapping architecture combining an atom chip with a printed circuit board, we continuously adjust the system's dimensionality over a wide range while measuring the phase fluctuations through the power spectrum of density ripples in time-of-flight expansion. Our measurements confirm that the chemical potential μ controls the departure of the system from 3D and that the fluctuations are dependent on both μ and the temperature T. Through a rigorous study we quantitatively observe how inside the crossover the dependence on T gradually disappears as the system becomes 3D. Throughout the entire crossover the fluctuations are shown to be determined by the relative occupation of 1D axial collective excitations.

The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor XY model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional XY has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, σ, in which there are a magnetized, a disordered and a critical phase [1]. Here we address the issue of whether the critical behavior of the two-dimensional XY model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range XY model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for σ < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1/r2 interactions.

We study the effective dynamics of ferromagnetic spin chains in presence of long-range interactions. We consider the Heisenberg Hamiltonian in one dimension for which the spins are coupled through power-law long-range exchange interactions with exponent α. We add to the Hamiltonian an anisotropy in the z-direction. In the framework of a semiclassical approach, we use the Holstein–Primakoff transformation to derive an effective long-range discrete nonlinear Schrödinger equation. We then perform the continuum limit and we obtain a fractional nonlinear Schrödinger-like equation. Finally, we study the modulational instability of plane-waves in the continuum limit and we prove that, at variance with the short-range case, plane waves are modulationally unstable for α<3. We also study the dependence of the modulation instability growth rate and critical wave-number on the parameters of the Hamiltonian and on the exponent α.