arXiv subjects

Javier Molina-Vilaplana

Publications and source records attributed to Javier Molina-Vilaplana.

At least 19 recordsLinked to original sources

arXiv2026

Monogamous quantum corrections to holographic mutual information

We construct an extensive model of bulk mutual information (MI) in anti-de Sitter spacetime and use it to describe the leading quantum corrections to the MI of certain holographic theories. The equivalence between bulk and boundary MI follows from the Faulkner--Lewkowycz--Maldacena prescription. We show that the extensivity of the bulk MI is sufficient for the quantum-corrected boundary entropy vector to satisfy monogamy of MI and all other holographic entropy cone inequalities. Our model is built from a covariantly conserved current-current kernel in AdS and is realized explicitly by a free massive Dirac fermion, whose boundary MI at long distances is that of a fermionic generalized free field (GFF). The construction also reproduces the expected short-distance divergence structure of a GFF, and the current-current correlator defines a positive and monotonically decreasing function along the renormalization-group flow. We illustrate this explicitly for disjoint half-disks at the conformal fixed point of the model in AdS$_3$, where we present the exact result.

hep-th↗

arXiv2026

Information Loss in Generalized Symmetry Breaking

We present an algebraic and information-theoretic framework for the breaking of generalized, non-invertible symmetries in $(2+1)$ dimensions. Such patterns are modeled as inclusions of finite-dimensional $C^*$-algebras equipped with conditional expectations, built upon a precise dictionary with anyon condensation in topological phases of matter. The conditional expectations are quantum channels that coarse-grain observables of the parent phase onto the symmetry-reduced condensed phase; their index --- a Watatani index equal to the quantum dimension of the condensate --- bounds, through its logarithm, the relative entropy between a state and its condensed image. This relative entropy serves as an entropic order parameter quantifying the information lost in the symmetry-reduction transition. We illustrate the framework with explicit examples: the toric code, abelian groups $Z_N$, and the representation category Rep$(S_3)$. Our results strengthen the connections between operator algebras and quantum information in the study of generalized symmetries.

quant-ph↗

arXiv2026

Entropic order parameters and topological holography

We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken symmetries. Various examples of group and non-invertible symmetries are studied. In particular, the origin of the distinguishability of the vacua resulting from spontaneously broken non-invertible symmetries is made manifest with an information-theoretic perspective, where certain operators in the SymTFT are excluded from observation.

hep-th↗

arXiv2024

Entropic Order Parameters for Categorical Symmetries in 2D-CFT

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (1 + 1)-d rational conformal field theories (RCFT). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (1 + 1)-d theories with categorical symmetries.

hep-th↗

arXiv2024

Generalized Symmetry Resolution of Entanglement in CFT for Twisted and Anyonic sectors

A comprehensive symmetry resolution of the entanglement entropy (EE) in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries is presented. This amounts to symmetry resolving the entanglement with respect to the generalized twisted and anyonic charge sectors of the theory. The anyonic sectors label the irreducible representations of a modular fusion category defining the symmetry and can be understood through the $(2+1)$-d symmetry topological field theory (SymTFT) that encodes the symmetry features of the CFT. Using this, we define the corresponding generalized boundary dependent charged moments necessary for the symmetry resolution of the entanglement entropy, which is the main result of this work. Furthermore, contrary to the case of invertible symmetries, we observe the breakdown of entanglement equipartition between different charged sectors at the next-to-leading order in the ultraviolet cutoff.

hep-th↗

arXiv2024

Fracton-elasticity duality on curved manifolds

The mechanical properties of crystals on curved substrates mix elastic, geometric and topological degrees of freedom. In order to elucidate the properties of such crystals we formulate the low-energy effective action that combines metric degrees of freedom with displacement fields and defects. We propose dualities for elasticity coupled to curved geometry formulated in terms of tensor gauge theories. We show that the metric degrees of freedom, evolving akin to linearized gravity are mapped to tensors with three indices. When coupled to crystals these degrees of freedom become gapped and, in the presence of dislocations and disclinations, multivalued. The elastic degrees of freedom remain gapless and mapped to symmetric gauge fields with two indices. In analogy with elasticity on flat space formulation we assume that the trace of the total quadrupole moment is conserved. In the dual formulation, topological defects, which act as sources for the gauge fields, are fractons or excitations with restricted mobility. This leads to generalized glide constraints that restrict both displacement and gravitational defects.

hep-th↗

arXiv2023

A post-Gaussian approach to dipole symmetries and interacting fractons

We use a post-Gaussian variational approach to non-perturbatively study a general class of interacting bosonic quantum field theories with generalized dipole symmetries and fractonic behaviour. We find that while a Gaussian approach allows to carry out a consistent renormalization group (RG) flow analysis of these theories, this only grasps the interaction terms associated to the longitudinal motion of dipoles, which is consistent with previous analysis using large $N$ techniques. Remarkably, our post-Gaussian proposal, by providing a variational improved effective potential, is able to capture the transverse part of the interaction between dipoles in such a way that a non trivial RG flow for this term is obtained and analyzed. Our results suggest that dipole symmetries that manifest due to the strong coupling of dipoles, may robustly emerge at low energies from short distance models without that symmetry.

hep-th↗

arXiv2022

Non-Gaussian Variational Wavefunctions for Interacting Bosons on the Lattice

A variational method for studying the ground state of strongly interacting quantum many-body bosonic systems is presented. Our approach constructs a class of extensive variational non-Gaussian wavefunctions which extend Gaussian states by means of nonlinear canonical transformations (NLCT) on the fields of the theory under consideration. We illustrate this method with the one dimensional Bose-Hubbard model for which the proposal presented here, provides a family of approximate ground states at arbitrarily large values of the interaction strength. We find that, for different values of the interaction, the non-Gaussian NLCT-trial states sensibly improve the ground state energy estimation when the system is in the Mott phase.

cond-mat.str-el↗

arXiv2022

Entanglement Renormalization of a $T\bar{T}$-deformed CFT

In this work we use cMERA, a continuous tensor network, to find a Gaussian approximation to the ground state of a $T\bar{T}$-deformed scalar CFT on the line, to first order in the deformation parameter. The result is used to find the correction to the correlators of scaling operators of the theory and to the entanglement entropy of a half-line. From the latter, we discuss the non-localities induced by the $T\bar{T}$-deformation at short length scales. We find that the kind of non-locality generated by those terms can be considered as a mild-one, in the sense that it does not violate the area law of entanglement. In the context of the conjectured connection between cMERA and holography, we find that at first insight a finite bulk radius can be defined in the putative geometric dual description of cMERA. However, the entropy analysis contradicts the proposal that no geometry can be ascribed to the region outside this radial cutoff.

hep-th↗

arXiv2022

The Large $N$ Limit of icMERA and Holography

In this work, we compute the entanglement entropy in continuous icMERA tensor networks for large $N$ models at strong coupling. Our results show that the $1/N$ quantum corrections to the Fisher information metric (interpreted as a local bond dimension of the tensor network) in an icMERA circuit, are related to quantum corrections to the minimal area surface in the Ryu-Takayanagi formula. Upon picking two different non-Gaussian entanglers to build the icMERA circuit, the results for the entanglement entropy only differ at subleading orders in $1/G_N$, i.e, at the structure of the quantum corrections in the bulk. The fact that the large $N$ part of the entropy can be always related to the leading area term of the holographic calculation is very suggestive. These results, constitute the first tensor network calculations at large $N$ and strong coupling simultaneously, pushing the field of tensor network descriptions of the emergence of dual spacetime geometries from the structure of entanglement in quantum field theory.

hep-th↗

arXiv2021

On the Entanglement Entropy in Gaussian cMERA

The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the entanglement entropy of the half space for a free scalar theory through a Gaussian cMERA circuit. We obtain the correct entropy written in terms of the optimized cMERA variational parameter, the local density of disentanglers. Accordingly, using the entanglement entropy production per unit scale, we study local areas in the bulk of the tensor network in terms of the differential entanglement generated along the cMERA flow. This result spurs us to establish an explicit relation between the cMERA variational parameter and the radial component of a dual AdS geometry through the Ryu-Takayanagi formula. Finally, based on recent formulations of non-Gaussian cMERA circuits, we argue that the entanglement entropy for the half space can be written as an integral along the renormalization scale whose measure is given by the Fisher information metric of the cMERA circuit. Consequently, a straightforward relation between AdS geometry and the Fisher information metric is also established.

hep-th↗

arXiv2021

Entanglement Entropy: Non-Gaussian States and Strong Coupling

In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability \emph{bonanza} shown by these variational \emph{ansatze} allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the $ϕ^4$ scalar field theory in 2D. Finally, we analyze the rôle played by higher order correlators in our results and show that strong subadditivity is satisfied.

hep-th↗

arXiv2020

Quantum Pontryagin Principle under Continuous Measurements and Feedback

In this note we develop the theory of the quantum Pontryagin principle for continuous measurements and feedback. The analysis is carried out under the assumption of compatible events in the output channel. The plant is a quantum system, which generally is in a mixed state, coupled to a continuous measurement channel. The Pontryagin Maximum Principle is derived in both the Schrödinger picture and Heisenberg picture, in particular in statistical moment coordinates. To avoid solving stochastic equations we derive a LQG scheme which is more suitable for control purposes.

eess.SY↗

arXiv2020

Non-Gaussian Entanglement Renormalization for Quantum Fields

In this work, a non-Gaussian cMERA tensor network for interacting quantum field theories (icMERA) is presented. This consists of a continuous tensor network circuit in which the generator of the entanglement renormalization of the wavefunction is nonperturbatively extended with nonquadratic variational terms. The icMERA circuit nonperturbatively implements a set of scale dependent nonlinear transformations on the fields of the theory, which suppose a generalization of the scale dependent linear transformations induced by the Gaussian cMERA circuit. Here we present these transformations for the case of self-interacting scalar and fermionic field theories. Finally, the icMERA tensor network is fully optimized for the $λϕ^4$ theory in $(1+1)$ dimensions. This allows us to evaluate, nonperturbatively, the connected parts of the two- and four-point correlation functions. Our results show that icMERA wavefunctionals encode proper non-Gaussian correlations of the theory, thus providing a new variational tool to study phenomena related with strongly interacting field theories.

hep-th↗

arXiv2019

Entanglement Renormalization for Interacting Field Theories

A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through a class of variational non-Gaussian wavefunctionals for which expectation values of local operators can be efficiently calculated analytically and in a closed form. The method consists of a series of scale-dependent nonlinear canonical transformations on the fields of the theory under consideration. Here, the $λ\, ϕ^4$ and the sine-Gordon scalar theories are used to illustrate how non-perturbative effects far beyond the Gaussian approximation are obtained by considering the energy functional and the correlation functions of the theory.

hep-th↗

arXiv2019

Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the quantum work distribution associated with the driving of chaotic quantum systems described by random matrix Hamiltonians and characterize exactly the work statistics associated with a sudden quench for arbitrary temperature and system size. Knowledge of the work statistics yields the Loschmidt echo dynamics of an entangled state between two copies of the system of interest, the thermofield double state. This echo dynamics is dictated by the spectral form factor. We discuss its relation to frame potentials and its use to assess information scrambling.

quant-ph↗

arXiv2018

Quantum work statistics, Loschmidt echo and information scrambling

A universal relation is established between the quantum work probability distribution of an isolated driven quantum system and the Loschmidt echo dynamics of a two-mode squeezed state. When the initial density matrix is canonical, the Loschmidt echo of the purified double thermofield state provides a direct measure of information scrambling and can be related to the analytic continuation of the partition function. Information scrambling is then described by the quantum work statistics associated with the time-reversal operation on a single copy, associated with the sudden negation of the system Hamiltonian.

quant-ph↗

arXiv2018

A Gaussian Variational Approach to cMERA for Interacting Fields

We use the Gaussian variational principle to apply cMERA to interacting quantum field theories in arbitrary spacetime dimensions. By establishing a correspondence between the first two terms in the variational expansion and the Gaussian Effective Potential, we can exactly solve for a variational approximation to the cMERA entangler. As examples, we treat scalar $φ^4$ theory and the Gross-Neveu model and extract non-perturbative behavior. We also comment on the connection between generalized squeezed coherent states and more generic entanglers.

hep-th↗