arXiv subjects

G. A. P. Ribeiro

Publications and source records attributed to G. A. P. Ribeiro.

At least 19 recordsLinked to original sources

arXiv2026

Correlation functions of the 19-vertex IRF model and its integrable quantum spin-1 chain

We consider the interaction-round-a-face version of the nineteen-vertex model and derive a new quantum spin-$1$ chain. In the isotropic limit, the associated spin chain can be seen as three coupled Babujian-Taktahjan spin chains with different boundary twists. We compute the ground state short-distance correlation functions of the isotropic model in the thermodynamic limit by exploiting the shared integrable structure between the models.

nlin.SI↗

arXiv2025

Teleportation based detection of quantum critical points using small spin chains

We show for the models here investigated that the teleportation based quantum critical point (QCP) detectors can properly estimate the locations of the QCPs when we are not even close to the thermodynamic limit (infinite spin chains) and when we only have access to finite temperature data. Specifically, by working with spin chains with about ten qubits and in equilibrium with a thermal reservoir at temperature T, we show that it is possible to locate with an error of only a few percents the correct spots of the QCPs for almost all the models studied here. The spin chains we investigate are given by the XXZ model with or without an external longitudinal magnetic field as well as the XX model, the XY model, and the Ising model, all of them subjected to an external transverse magnetic field.

quant-ph↗

arXiv2025

Finite temperature detection of quantum critical points via internal quantum teleportation

We show that the teleportation protocol can be efficiently used to detect quantum critical points using finite temperature data even if all resources needed to its implementation lie within the system under investigation. Contrary to a previous proposal, there is no need to use an external qubit as the input state to be teleported to one of the qubits within the system. Here, we use a pair of nearest neighbor spins from an infinite spin-1/2 chain in equilibrium with a heat bath as the entangled resource of the quantum teleportation protocol and a third adjacent qubit within the chain itself as the input state to be teleported. For several spin chain models subjected to an external magnetic field, we show that the efficiency of the teleportation protocol is severely affected as we cross the quantum critical points associated with those spin chains. This abrupt change in efficiency gives us a clear indication of a quantum phase transition.

quant-ph↗

arXiv2024

Correlation functions of the six-vertex IRF model and its quantum spin chain

We consider the interaction-round-a-face version of the isotropic six-vertex model. The associated spin chain is made of two coupled Heisenberg spin chains with different boundary twists. The phase diagram of the model and the long distance correlations were studied in [Nucl. Phys. B, 995 (2023) 116333]. Here, we compute the short-distance correlation functions of the model in the ground state for finite system sizes via non-linear integral equations and in the thermodynamic limit. This was possible since the model satisfies the face version of the discrete quantum Knizhnik-Zamolodchikov (qKZ) equation. A suitable ansatz for the density matrix is proposed in the form of a direct sum of two Heisenberg density matrices, which allows us to obtain the discrete functional equation for the two-site function $ω(λ_1,λ_2)$. Thanks to the known results on the factorization of correlation functions of the Heisenberg chain, we are able to compute the density matrix of the IRF model for up to four sites and its associated spin chain for up to three sites.

math-ph↗

arXiv2024

Finite temperature detection of quantum critical points: a comparative study

We comparatively study three of the most useful quantum information tools to detect quantum critical points (QCPs) when only finite temperature data are available. We investigate quantitatively how the quantum discord, the quantum teleportation based QCP detectors, and the quantum coherence spectrum pinpoint the QCPs of several spin-$1/2$ chains. We work in the thermodynamic limit (infinite number of spins) and with the spin chains in equilibrium with a thermal reservoir at temperature $T$. The models here studied are the $XXZ$ model with and without an external longitudinal magnetic field, the Ising transverse model, and the $XY$ model subjected to an external transverse magnetic field.

quant-ph↗

arXiv2024

Detecting quantum critical points at finite temperature via quantum teleportation: further models

In [Phys. Rev. A 107, 052420 (2023)] we showed that the quantum teleportation protocol can be used to detect quantum critical points (QCPs) associated with a couple of different classes of quantum phase transitions, even when the system is away from the absolute zero temperature (T=0). Here, working in the thermodynamic limit (infinite chains), we extend the previous analysis for several other spin-1/2 models. We investigate the usefulness of the quantum teleportation protocol to detect the QCPs of those models when the temperature is either zero or greater than zero. The spin chains we investigate here are described by the XXZ model, the XY model, and the Ising model, all of them subjected to an external magnetic field. Specifically, we use a pair of nearest neighbor qubits from an infinite spin chain at thermal equilibrium with a reservoir at temperature T as the resource to execute the quantum teleportation protocol. We show that the ability of this pair of qubits to faithfully teleport an external qubit from the chain is dramatically affected as we cross the QCPs related to the aforementioned models. The results here presented together with the ones of [Phys. Rev. A 107, 052420 (2023)] suggest that the quantum teleportation protocol is a robust and quite universal tool to detect QCPs even when the system of interest is far from the absolute zero temperature.

quant-ph↗

arXiv2023

Finite temperature properties of an integrable zigzag ladder chain

We consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin interactions. We apply the quantum transfer matrix approach for the face model version of the six-vertex model. The integrable quantum Hamiltonian shares some thermodynamical properties with the Heisenberg XXZ chain, but has different ordering and critical exponents. Two gapped phases are the dimerized antiferromagnetic order and the usual antiferromagnetic (Néel) order for positive nearest neighbour Ising coupling. In between these, there is an extended critical region, which is a quantum spin-liquid with broken parity symmetry inducing an oscillatory behavior at the long distance $<σ_1^zσ_{\ell+1}^z>$ correlation. At finite temperatures, the numerical solution of the non-linear integral equations allows for the determination of the correlation length as well as for the momentum of the oscillation.

math-ph↗

arXiv2023

Detecting quantum critical points at finite temperature via quantum teleportation

We show that the quantum teleportation protocol is a powerful tool to study quantum phase transitions (QPTs) at finite temperatures. We consider a pair of spins from an infinite spin-1/2 chain (XXZ model) in equilibrium with a reservoir at temperature T as the resource used by Alice and Bob to implement the teleportation protocol. We show that the efficiency of this pair of spins to teleport a qubit is drastically affected after we cross a quantum critical point (QCP), even for high values of T. Also, we show that the present tool is as sharp as quantum discord (QD) to spotlight a QCP, where QD is the best finite T QCP detector known to date. Contrary to QD, however, we show that the present tool is easier to compute theoretically and has a direct experimental and operational meaning.

cond-mat.str-el↗

arXiv2022

On the partition function of the $Sp(4)$ integrable vertex model

In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under $Sp(4)$ symmetry. We establish a set of functional relations which include a transfer matrix inversion identity. The solution of these relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental $Sp(4)$ representation of the vertex model. As a byproduct we also obtain the partition function per site of a vertex model mixing the four and five dimensional representations of the $Sp(4)$ symmetry.

math-ph↗

arXiv2022

On the partition function of the $Sp(2n)$ integrable vertex model

We study the partition function per site of the integrable $Sp(2n)$ vertex model on the square lattice. We establish a set of transfer matrix fusion relations for this model. The solution of these functional relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental $Sp(2n)$ representation of the vertex model. In addition, we also obtain the partition function of vertex models mixing the fundamental with other representations.

math-ph↗

arXiv2020

Correlation functions of integrable $O(n)$ spin chains

We study the correlation functions of the integrable $O(n)$ spin chain in the thermodynamic limit. We addressed the problem of solving functional equations of the quantum Knizhnik Zamolodchikov type for density matrix related to the $O(n)$ spin chain. We give the explicit solution for two-sites density matrix elements for the $O(n)$ which are then evaluated for the $n=3,4,\dots,8$ cases at zero temperature.

math-ph↗

arXiv2019

Arctic curve of the free-fermion six-vertex model with reflecting end boundary condition

We consider the six-vertex model with reflecting end boundary condition. We study the asymptotic behavior of the boundary correlations. This asymptotic behavior is used as an input into the Tangent Method in order to derive analytically the arctic curve at the free fermion point. The obtained curve is a semicircle, which is in agreement with previous Monte Carlo simulations.

math-ph↗

arXiv2019

Boundary correlations for the six-vertex model with reflecting end boundary condition

We consider the six-vertex model with reflecting end boundary condition. We compute analytically boundary correlation functions, such as the boundary polarization and the emptiness formation probability. In order to do that, we use the Sklyanin's reflection algebra to derive recursion relations for the partition function of the model as well as for the boundary correlations in terms of the partition function. Thanks to the Tsuchiya determinant formula, these recursion relations allow the boundary correlations to be also efficiently written in determinantal form.

math-ph↗

arXiv2019

Correlation functions of the integrable $SU(n)$ spin chain

We study the correlation functions of $SU(n)$ $n>2$ invariant spin chains in the thermodynamic limit. We formulate a consistent framework for the computation of short-range correlation functions via functional equations which hold even at finite temperature. We give the explicit solution for two- and three-site correlations for the $SU(3)$ case at zero temperature. The correlators do not seem to be of factorizable form. From the two-sites result we see that the correlation functions are given in terms of Hurwitz' zeta function, which differs from the $SU(2)$ case where the correlations are expressed in terms of Riemann's zeta function of odd arguments.

math-ph↗

arXiv2018

Phase separation in the six-vertex model with a variety of boundary conditions

We present numerical results for the six-vertex model with a variety of boundary conditions. Adapting an algorithm proposed by Allison and Reshetikhin for domain wall boundary conditions, we examine some modifications of these boundary conditions. To be precise, we discuss partial domain wall boundary conditions, reflecting ends and half turn boundary conditions (domain wall boundary conditions with half turn symmetry).

cond-mat.stat-mech↗

arXiv2017

Finite size and finite temperature studies of the $osp(1|2)$ spin chain

We study a quantum spin chain invariant by the superalgebra $osp(1|2)$. We derived non-linear integral equations for the row-to-row transfer matrix eigenvalue in order to analyze its finite size scaling behaviour and we determined its central charge. We have also studied the thermodynamical properties of the obtained spin chain via the non-linear integral equations for the quantum transfer matrix eigenvalue. We numerically solved these NLIE and evaluated the specific heat and magnetic susceptibility. The analytical low temperature analysis was performed providing a different value for the effective central charge. The computed values are in agreement with the numerical predictions in the literature.

nlin.SI↗

arXiv2016

Exact thermodynamics and phase diagram of integrable t-J model with chiral interaction

We study the phase diagram and finite temperature properties of an integrable generalization of the one-dimensional super-symmetric t-J model containing interactions explicitly breaking parity-time reversal (PT) symmetries. To this purpose, we apply the quantum transfer matrix method which results in a finite set of non-linear integral equations. We obtain numerical solutions to these equations leading to results for thermodynamic quantities as function of temperature, magnetic field, particle density and staggering parameter. Studying the maxima lines of entropy at low but non zero temperature reveals the phase diagram of the model. There are ten different phases which we may classify in terms of the qualitative behaviour of auxiliary functions, closely related to the dressed energy functions.

cond-mat.stat-mech↗

arXiv2016

Correlation functions of the integrable spin-s chain

We study the correlation functions of su(2) invariant spin-s chains in the thermodynamic limit. We derive non-linear integral equations for an auxiliary correlation function $ω$ for any spin s and finite temperature T. For the spin-3/2 chain for arbitrary temperature and zero magnetic field we obtain algebraic expressions for the reduced density matrix of two-sites. In the zero temperature limit, the density matrix elements are evaluated analytically and appear to be given in terms of Riemann's zeta function values of even and odd arguments.

cond-mat.stat-mech↗