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This study explores the semiclassical limit of an integrable-chaotic bosonic many-body quantum system, providing nuanced insights into its behavior. We examine classical-quantum correspondences across different interaction regimes of bosons in a triple-well potential, ranging from the integrable to the self-trapping regime, and including the chaotic one. The close resemblance between the phase-space mean projections of classical trajectories and those of Husimi distributions evokes the Principle of Uniform Semiclassical Condensation (PUSC) of Wigner functions of eigenstates. Notably, the resulting figures also exhibit patterns reminiscent of Jason Gallas's "shrimp" shapes., Comment: 8 pages, 9 figures

The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. A numerical framework for these inner products is devised. Causality is also explicitly checked by a numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter., Comment: 6 pages, revised version. Accepted for publication in PRD

The interaction between Unruh-De Witt spin $1/2$ detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom. The resulting density matrix is employed to the study of the Bell-CHSH correlator. It turns out that, as a consequence of the interaction with the quantum field, the violation of the Bell-CHSH inequality exhibits a decreasing as compared to the case in which the scalar field is absent., Comment: 8 pages, 3 figures. Final version, to appear in JHEP

Mermin's inequalities are investigated in a Quantum Field Theory framework by using von Neumann algebras built with Weyl operators. We devise a general construction based on the Tomita-Takesaki modular theory and use it to compute the vacuum expectation value of the Mermin operator, analyzing the parameter space and explicitly exhibiting a violation of Mermin's inequalities. Therefore, relying on the power of modular operators, we are able to demonstrate that Mermin's inequalities are violated when examined within the vacuum state of a scalar field theory., Comment: 8 pages, 1 figure, revised version. Accepted for publication in PRD

In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to chaos in classical dynamics is visualized through Poincar\'e sections. Classical trajectories in phase space closely resemble the projections of the Husimi functions of eigenstates with similar energy, even in chaotic cases. It is demonstrated that this correlation is more evident when projecting the eigenstates onto the Fock states. The analysis is carried out at a critical energy where the eigenstates are maximally delocalized in the Fock basis. Despite the imperfect delocalization, its influence is present in the classical and quantum properties under investigation. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells, even within the chaotic region., Comment: 14 pages, 19 figures

We devise a general setup to investigate the violation of the Bell-CHSH inequality in the vacuum state in the context of Quantum Field Theory. We test the method with massless spinor fields in $(1+1)$-dimensional Minkowski space-time. Alice's and Bob's test functions are explicitly constructed, first by employing Haar wavelets which are then bumpified into proper test functions via a smoothening procedure relying on the Planck-taper window function. Relativistic causality is implemented by requiring the support of Alice's and Bob's test functions to be located in the left and right Rindler wedges, respectively. Violations of the Bell-CHSH inequality as close as desired to Tsirelson's bound are reported. We briefly comment on the extra portal, compared to earlier works, this opens to scrutinize Bell-CHSH inequalities with generic, interacting Quantum Field Theories., Comment: 7 pages, 2 figures. Published in PRD

The violation of Mermin's inequalities is analyzed by making use of two different Bell setups built with pseudospin operators. Employing entangled states defined by means of squeezed and coherent states, the expectation value of Mermin's polynomials $M_n$ is evaluated for $n=3$ and $n=4$. In each case, we analyze the correlator $\langle M_n \rangle$ and identify the set of parameters leading to the violation of Mermin's inequalities and to the saturation of the bound predicted by Quantum Mechanics., Comment: 10 pages, 16 figures

A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum $| 0 \rangle$, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states., Comment: 8 pages, published in PLB

In this work, using a NISQ framework, we obtain the gap of a BCS Hamiltonian. This could lead to interesting implications for superconductivity research. For such task, we choose to use the Variational Quantum Deflation and analyze the hardware restrictions that are needed to find the energy spectra on current quantum hardware. We also compare two different kinds of classical optimizers, Constrained Optimization BY Linear Approximations (COBYLA) and Simultaneous Perturbation Stochastic Approximation (SPSA), and study the effect of decoherence caused by the presence of noise when using simulations in real devices. We implement this method for a system with both 2 and 5 qubits. Furthermore, we show how to approximate the gap within one standard deviation, even with the presence of noise., Comment: 17 pages, 14 figures, Appendix

We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions are found for an arbitrary number of external legs, and a general algorithm is implemented for this calculus. From these solutions, we calculate many asymptotics expansion terms for a simple analytical tool (Taylor expansion theorem). Our approach offers new perspectives in the realm of Feynman diagrams enumeration (or zero-dimensional quantum field theory)., Comment: 17 pages, 1 figure

Quantum computing, along with quantum metrology and quantum communication, are disruptive technologies that promise, in the near future, to impact different sectors of academic research and industry. Among the computational challenges with great interest in science and industry are the inversion problems. These kinds of numerical procedures can be described as the process of determining the cause of an event from measurements of its effects. In this paper, we apply a recursive quantum algorithm to a D-Wave quantum annealer to solve a small scale seismic inversions problem. We compare the obtained results from the quantum computer to those derived from a classical algorithm. The accuracy achieved by the quantum computer is at least as good as that of the classical computer.

We focus on using an architecture similar to the $\beta$-Variational Autoencoder ($\beta$-VAE) to discriminate if a quantum state is entangled or separable based on measurements. We split the data into two sets, the set of local and correlated measurements. Using the latent space, which is a low dimensional representation of the data, we show that restricting ourselves to the set of local data it is not possible to distinguish between entangled and separable states. Meanwhile, when considering both correlated and local measurements, an accuracy of over 80% is attained in the structure of the latent space., Comment: 5 pages, 4 figures

In this work, we generalize a recursive enumerative formula for connected Feynman diagrams with two external legs. The Feynman diagrams are defined from a fermionic gas with a two-body interaction. The generalized recurrence is valid for connected Feynman diagrams with an arbitrary number of external legs and an arbitrary order. The recurrence formula terms are expressed in function of weak compositions of non-negative integers and partitions of positive integers in such a way that to each term of the recurrence correspond a partition and a weak composition. The foundation of this enumeration is the Wick theorem, permitting an easy generalization to any quantum field theory. The iterative enumeration is constructive and enables a fast computation of the number of connected Feynman diagrams for a large amount of cases. In particular, the recurrence is solved exactly for two and four external legs, leading to the asymptotic expansion of the number of different connected Feynman diagrams., Comment: 24 pages, 14 figures

Multiparticle entangled states, essential ingredients for modern quantum technologies, are routinely generated in experiments of atomic Bose-Einstein condensates (BECs). However, the entanglement in ultracold interacting Fermi gases has not been yet exploited. In this work, by using an ansatz of composite bosons, we show that many-particle entanglement between two fermionic ensembles localized in spatially separated modes can be generated by splitting an ultracold interacting Fermi gas in the (molecular) BEC regime. This entanglement relies on the fundamental fermion exchange symmetry of molecular constituents and might be used for implementing Bell test of quantum nonlocality in oncoming experiments., Comment: 9 pages, 5 figures

From the standard procedure for constructing Feynman vacuum graphs in $\phi^4$ theory from the generating functional $Z$, we find a relation with sets of certain combinatorial matrices, which allows us to generate the set of all Feynman graphs and the respective multiplicities in an equivalent combinatoric way. These combinatorial matrices are explicitly related with the permutation group, which facilitates the construction of the vacuum Feynman graphs. Various insights in this combinatoric problem are proposed, which in principle provide an efficient way to compute the Feynman vacuum graphs and its multiplicities., Comment: 27 pages

We show that an ansatz based on independent composite bosons [Phys. Rep. 463, 215 (2008)] accurately describes the condensate fraction of molecular Bose-Einstein condensates in ultracold Fermi gases. The entanglement between the fermionic constituents of a single Feshbach molecule then governs the many-particle statistics of the condensate, from the limit of strong interaction to close to unitarity. This result strengthens the role of entanglement as the indispensable driver of composite-boson behavior. The condensate fraction of fermion pairs at zero temperature that we compute matches excellently previous results obtained by means of fixed-node diffusion Monte Carlo methods and the Bogoliubov depletion approximation. This paves the way towards the exploration of the BEC-BCS crossover physics in mixtures of cold Fermi gases with an arbitrary number of fermion pairs as well as the implementation of Hong-Ou-Mandel-like interference experiments proposed within coboson theory., Comment: 9 pages, 5 figures

We study three dimensional Bose and Fermi gases in the upper branch, a phase defined by the absence of bound states in the repulsive interaction regime, within an approximation that considers only two-body interactions. Employing a formalism based on the S-matrix, we derive useful analytic expressions that hold on the upper branch in the weak coupling limit. We determine upper branch phase diagrams for both bosons and fermions with techniques valid for arbitrary positive scattering length., Comment: 5 pages, 4 figures. v3: published version

Memoryless time evolutions are ubiquitous in nature but often correspond to a resolution-induced approximation, i.e. there are correlations in time whose effects are undetectable. Recent advances in the dynamical control of small quantum systems provide the ideal scenario to probe some of these effects. Here we experimentally demonstrate the precise induction of memory effects on the evolution of a quantum coin (qubit) by correlations engineered in its environment. In particular, we design a collisional model in Nuclear Magnetic Resonance (NMR) and precisely control the strength of the effects by changing the degree of correlation in the environment and its time of interaction with the qubit. We also show how these effects can be hidden by the limited resolution of the measurements performed on the qubit. The experiment reinforces NMR as a test bed for the study of open quantum systems and the simulation of their classical counterparts.

We investigate by means of a variational approach the effective potential of a 5D U(1) scalar model at finite temperature and compactified on S^1 and S^1/Z_2 as well as the corresponding 4D model obtained through a trivial dimensional reduction. We are particularly interested in the behaviour of the thermal masses of the scalar field with respect to the Wilson line phase and the results obtained are compared with those coming from a one-loop effective potential calculation. We also explore the nature of the phase transition.

We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed., Comment: 13 pages

We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many body processes that are reducible to 2-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons, and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a meta-stable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length., Comment: 22 pages, 8 figures. Version 2: 1 additional reference (only change)

We study the field-induced quantum phase transitions (QPT) and the relevant magnetic properties of a spin-1/2 two-leg integrable spin ladder (ISL), of which the system parameters in bridging to the real compounds are determined by setting the extra interactions in the Hamiltonian of the ISL relative to the Heisenberg spin ladder to vanish in the expectation in the ground state (GS). Such an ISL analytically has the correct leading terms of both the critical fields of the two QPT's as in the real strongly-coupled compounds: g\mu _BH_{c1}=J_{\perp}-J_{\parallel} and g\mu_BH_{c2}=J_{\perp}+2J_{\parallel} in terms of the experimental leg (J_{\parallel}) and rung (J_{\perp}) interactions. The symmetric magnetization inflection point is located at g\mu _BH_{IP}=J_{\perp}+J_{\parallel}/2. The magnetizations for the GS and at finite temperatures, as well as the susceptibility, show good agreements in various comparisons with the finite-site exact diagonalization, the transfer-matrix renormalization group numerical result, the perturbation theory, and the compounds (5IAP)_2CuBr_4\cdot 2H_2O, Cu_2(C_5H_{12}N_2)_2Cl_4 and (C_5H_{12}N)_2CuBr_4., Comment: 11 pages, 8 figures

We study an integrable two-leg spin-1/2 ladder with an XYZ-type rung interaction. Exact rung states and rung energies are obtained for the anisotropic rung coupling in the presence of a magnetic field. Magnetic properties are analyzed at both zero and finite temperatures via the thermodynamic Bethe ansatz and the high-temperature expansion. According to different couplings in the anisotropic rung interaction, there are two cases in which a gap opens, with the ground state involving one or two components in the absence of a magnetic field. We obtain the analytic expressions of all critical fields for the field-induced quantum phase transitions (QPT). Anisotropic rung interaction leads to such effects as separated magnetizations and susceptibilities in different directions, lowered inflection points and remnant weak variation of the magnetization after the last QPT., Comment: 9 pages, 8 figures; a typo in C_2(below eq.7) corrected

By introducing a basis for a novel realization of the SU(4) Lie algebra, we exactly solve a spin-orbital chain with one-ion $L$-$S$ coupling (OILSC) via the Bethe ansatz (BA) approach. In the context of different Land\'e $g$ factors of the spin and orbital sectors, the OILSC results in rich and novel quantum phase transitions. Some accurate analytical expressions for the critical fields are obtained. Both spin ordering and orbital ordering are found in a gapped singlet phase. The system exhibits many interesting phenomena such as nonvanishing magnetization of the singlet phase, multi-entrance of the singlet in the ground state when the field varies, unsymmetric magnetization in two-component phase and magnetization crossover for different OILSC., Comment: 5 pages, 2 figures

A spin-orbital chain with different Land\'e $g$ factors and one-ion anisotropy is studied in the context of the thermodynamical Bethe ansatz. It is found that there exists a magnetization plateau resulting from the different Land\'e $g$ factors. Detailed phase diagram in the presence of an external magnetic field is presented both numerically and analytically. For some values of the anisotropy, the four-component system undergoes five consecutive quantum phase transitions when the magnetic field varies. We also study the magnetization in various cases, especially its behaviors in the vicinity of the critical points. For the SU(4) spin-orbital model, explicit analytical expressions for the critical fields are derived, with excellent accuracy compared with numerics., Comment: 5 pages, 3 figures

We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras $U_{q}(\hat g)$. These algebras do not form a symmetry algebra of the model for generic values of the deformation parameter $q$ when periodic boundary conditions are imposed. If $q$ is evaluated at a root of unity we demonstrate that in certain commensurate sectors one can construct non-abelian subalgebras which are translation invariant and supercommute with the transfer matrix and therefore with all charges of the model. In the line of argument we introduce the restricted quantum superalgebra $U^{res}_q(\hat g)$ and investigate its root of unity limit. We prove several new formulas involving supercommutators of arbitrary powers of the Chevalley-Serre generators and derive higher order quantum Serre relations as well as an analogue of Lustzig's quantum Frobenius theorem for superalgebras., Comment: 31 pages, tcilatex (minor typos corrected)

We consider the repulsive Hubbard model in one dimension and show the different mechanisms present in the charge and spin separation phenomena for an electron, at half filling and bellow half filling. We also comment recent experimental results., Comment: revtex, 4 pages

The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for the energy is given., Comment: 7 pages (revtex), minor modifications. To appear in Mod. Phys. Lett. A

We present a new integrable model for correlated electrons which is based on a $so(5)$ symmetry. By using an $\eta$-pairing realization we construct eigenstates of the Hamiltonian with off-diagonal long-range order. It is also shown that these states lie in the ground state sector. We exactly solve the model on a one-dimensional lattice by the Bethe ansatz., Comment: RevTex, 4 pages

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models., Comment: 17 pages, RevTex