arXiv subjects

Giovanni Ramírez

Publications and source records attributed to Giovanni Ramírez.

9 recordsLinked to original sources

arXiv2023

Entanglement links and the quasiparticle picture

The time evolution of a quantum state with short-range correlations after a quench to a one-dimensional critical Hamiltonian can be understood using the quasi-particle picture, which states that local entanglement spreads as if it was carried by quasi-particles which separate at a fixed speed. We extend the quasi-particle picture using the recently introduced link representation of entanglement, allowing us to apply it to initial states presenting long-range correlations. The entanglement links are current correlators, and therefore follow a wave equation on the appropriate configurational space which allows us to predict the time evolution of the entanglement entropies. Our results are checked numerically for free fermionic chains with different initial entanglement patterns.

quant-ph↗

arXiv2022

Exotic correlation spread in free-fermionic states with initial patterns

We describe a relation between the light-cone velocities after a quantum quench and the internal structure of the initial state, in the particular case of free fermions on a chain at half filling. The considered states include short-range valence bond solids, i.e., dimerized states, and long-range states such as the rainbow. In all the considered cases the correlations spread into one or a few well-defined light cones, each of them presenting an effective velocity which can be read from the form factor. Interestingly, we find that the observed velocities range from zero to the Fermi velocity and may not always be obtained from the dispersion relation for valid momenta.

quant-ph↗

arXiv2018

Breaking the Area Law: The Rainbow State

An exponential deformation of a 1D critical Hamiltonian, with couplings falling on a length scale $h^{-1}$, gives rise to ground states whose entanglement entropy follows a volume law, i.e. the area law is violated maximally. The ground state is now in the so-called {\em rainbow phase}, where valence bonds connect sites on the left half with their symmetric counterparts on the right. Here we discuss some of the most relevant features of this rainbow phase, focusing on the XX and Heisenberg models. Moreover, we show that the rainbow state can be understood either as a thermo-field double of a conformal field theory with a temperature proportional to $h$ or as a massless Dirac fermion in a curved spacetime with constant negative curvature proportional to $h$. Finally, we introduce a study of the time-evolution of the rainbow state after a quench to a homogeneous Hamiltonian.

quant-ph↗

arXiv2018

Quantum Entanglement In Inhomogeneous 1D Systems

The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our inhomogeneous system, the inhomogeneity parameter, $h$, allows us to tune different regimes where a volumetric violation of the area law appears. We apply the strong disorder renormalization group to describe the maximally entangled state of the system in a strong inhomogeneity regime. Moreover, in a weak inhomogeneity regime, we use a continuum approximation to describe the state as a thermo-field double in a conformal field theory with an effective temperature which is proportional to the inhomogeneity parameter of the system. The latter description also shows that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature $R=-h^2$, providing another example of the relation between quantum entanglement and space-time geometry. The results we discuss here were already published before, but here we present a more didactic exposure of basic concepts of the rainbow system for the students attending the Latin American School of Physics Marcos Moshinsky 2017.

quant-ph↗

arXiv2016

More on the rainbow chain: entanglement, space-time geometry and thermal states

The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled. Here we show that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature $R=-h^2$ ($h$ is the amplitude of the inhomogeneity). This identification allows us to use recently developed techniques to study inhomogeneous conformal systems and to analytically characterise the entanglement entropies of more general bipartitions. These results are carefully tested against exact numerical calculations. Finally, we study the entanglement entropies of the rainbow chain in thermal states, and find that there is a non-trivial interplay between the rainbow effective temperature $T_R$ and the physical temperature $T$.

cond-mat.str-el↗

arXiv2016

Entanglement in correlated random spin chains, RNA folding and kinetic roughening

Average block entanglement in the 1D XX-model with uncorrelated random couplings is known to grow as the logarithm of the block size, in similarity to conformal systems. In this work we study random spin chains whose couplings present long range correlations, generated as gaussian fields with a power-law spectral function. Ground states are always planar valence bond states, and their statistical ensembles are characterized in terms of their block entropy and their bond-length distribution, which follow power-laws. We conjecture the existence of a critical value for the spectral exponent, below which the system behavior is identical to the case of uncorrelated couplings. Above that critical value, the entanglement entropy violates the area law and grows as a power law of the block size, with an exponent which increases from zero to one. Similar planar bond structures are also found in statistical models of RNA folding and kinetic roughening, and we trace an analogy between them and quantum valence bond states. Using an inverse renormalization procedure we determine the optimal spin-chain couplings which give rise to a given planar bond structure, and study the statistical properties of the couplings whose bond structures mimic those found in RNA folding.

cond-mat.stat-mech↗

arXiv2015

Entanglement over the rainbow

In one dimension the area law for the entanglement entropy is violated maximally by the ground state of a strong inhomogeneous spin chain, the so called concentric singlet phase (CSP), that looks like a rainbow connecting the two halves of the chain. In this paper we show that, in the weak inhomogeneity limit, the rainbow state is a thermofield double of a conformal field theory with a temperature proportional to the inhomogeneity parameter. This result suggests some relation of the CSP with black holes. Finally, we propose an extension of the model to higher dimensions.

quant-ph↗

arXiv2014

From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains

An exponential deformation of 1D critical Hamiltonians gives rise to ground states whose entanglement entropy satisfies a volume-law. This effect is exemplified in the XX and Heisenberg models. In the XX case we characterize the crossover between the critical and the maximally entangled ground state in terms of the entanglement entropy and the entanglement spectrum.

cond-mat.str-el↗

arXiv2014

Entanglement in low-energy states of the random-hopping model

We study the low-energy states of the 1D random-hopping model in the strong disordered regime. The entanglement structure is shown to depend solely on the probability distribution for the length of the effective bonds $P(l_b)$, whose scaling and finite-size behavior are established using renormalization-group arguments and a simple model based on random permutations. Parity oscillations are absent in the von Neumann entropy with periodic boundary conditions, but appear in the higher moments of the distribution, such as the variance. The particle-hole excited states leave the bond-structure and the entanglement untouched. Nonetheless, particle addition or removal deletes bonds and leads to an effective saturation of entanglement at an effective block size given by the expected value for the longest bond.

cond-mat.stat-mech↗