arXiv subjects

Ali Mollabashi

Publications and source records attributed to Ali Mollabashi.

30 records · Page 2Linked to original sources

arXiv2017

Entanglement in Lifshitz-type Quantum Field Theories

We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz scalar theory. We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the $z\to\infty$ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2+1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponents due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.

hep-th↗

arXiv2017

Holographic Subregion Complexity for Singular Surfaces

Recently holographic prescriptions are proposed to compute quantum complexity of a given state in the boundary theory. A specific proposal known as `holographic subregion complexity' is supposed to calculate the the complexity of a reduced density matrix corresponding to a static subregion. We study different families of singular subregions in the dual field theory and find the divergence structure and universal terms of holographic subregion complexity for these singular surfaces. We find that there are new universal terms, logarithmic in the UV cutoff, due to the singularities of a family of surfaces including a kink in (2+1)-dimension and cones in even dimensional field theories. We find examples of new divergent terms such as square logarithm and negative powers times the logarithm of the UV cut-off parameter.

hep-th↗

arXiv2016

Non-local Probes in Holographic Theories with Momentum Relaxation

We consider recently introduced solutions of Einstein gravity with minimally coupled massless scalars. The geometry is homogeneous, isotropic and asymptotically anti de-Sitter while the scalar fields have linear spatial-dependent profiles. The spatially-dependent marginal operators dual to scalar fields cause momentum dissipation in the deformed dual CFT. We study the effect of these marginal deformations on holographic entanglement measures and Wilson loop. We show that the structure of the universal terms of entanglement entropy for d(>2)-dim deformed CFTs is corrected depending on the geometry of the entangling regions. In d = 2 case, the universal term is not corrected while momentum relaxation leads to a non-critical correction. We also show that decrease of the correlation length causes: the phase transition of holographic mutual information to happen at smaller separations and the confinement/deconfinement phase transition to take place at smaller critical lengths. The effective potential between point like external objects also gets corrected. We show that the strength of the corresponding force between these objects is an increasing function of the momentum relaxation parameter.

hep-th↗

arXiv2016

On the Entanglement Between Interacting Scalar Field Theories

We study "field space entanglement" in certain quantum field theories consisting of N number of free scalar fields interacting with each other via kinetic mixing terms. We present exact analytic expressions for entanglement end Renyi entropies between arbitrary number of scalar fields by which we could explore certain entanglement inequalities. Other entanglement measures such as mutual information and entanglement negativity have also been studied. We also give some comments about possible holographic realizations of such models.

hep-th↗

arXiv2016

Holographic Mutual Information for Singular Surfaces

We study corner contributions to holographic mutual information for entangling regions composed of a set of disjoint sectors of a single infinite circle in three-dimensional conformal field theories. In spite of the UV divergence of holographic mutual information, it exhibits a first order phase transition. We show that tripartite information is also divergent for disjoint sectors, which is in contrast with the well-known feature of tripartite information being finite even when entangling regions share boundaries. We also verify the locality of corner effects by studying mutual information between regions separated by a sharp annular region. Possible extensions to higher dimensions and hyperscaling violating geometries is also considered for disjoint sectors.

hep-th↗

arXiv2014

Entanglement between Two Interacting CFTs and Generalized Holographic Entanglement Entropy

In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting $\mathcal{N}=4$ super Yang-Mills theories by introducing a minimal surface in the S$^5$ direction, instead of the AdS$_5$ direction. This offers a possible generalization of holographic entanglement entropy.

hep-th↗

arXiv2013

Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature

We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal of arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.

hep-th↗

arXiv2013

Crystalline Geometries from Fermionic Vortex Lattice

We study charged Dirac fermions on an AdS$_2\times R^2$ background with a non-zero magnetic field. Under certain boundary conditions, we show that the charged fermion can make the background unstable, resulting in spontaneously formation of a vortex lattice. We observe that an electric field emerges in the back-reacted solution due to the vortex lattice constructed from spin polarized fermions. This electric field may be extended to the UV boundary which leads to a finite charge density. We also discuss corrections to the thermodynamic functions due to the lattice formation.

hep-th↗

arXiv2013

Holographic quantum critical points in Lifshitz space-time

We study a minimally coupled charged scalar field in a charged Lifshitz background. For z=2, we find an analytic expression for the corresponding low energy retarded Green's function. Unlike the RN-AdS case, the position of the superfluid surfaces depends on the charge of the scalar field only through the IR scaling dimension. We show that by increasing the dynamical exponent, the dual theory becomes more stable. We also show that the background could suffer from an instability of the IR geometry leading to a bifurcating critical point. It also allows the existence of scalar hair, causing hybridized critical point. We have investigated stable an unstable regions in the parameter space.

hep-th↗

arXiv2012

Holographic Aspects of Two-charged Dilatonic Black Hole in AdS5

We study certain features of a strongly coupled theory whose gravitational dual is given by two-charge dilatonic black hole in AdS5 which has recently been used to study holographic Fermi liquids. By making use of the gravity description, we have studied conductivity, holographic entanglement entropy and dynamics of a charged scalar field. In particular at low energy we find that the temperature dependence of the real part of the conductivity goes as T^3 and the background is stable against scalar condensations.

hep-th↗

arXiv2012

Fermions on Lifshitz Background

We study a non-relativistic fermionic retarded Green's function by making use of a fermion on the Lifshitz geometry with critical exponent z = 2. With a natural boundary condition, respecting the symmetries of the model, the resultant retarded Green's function exhibits a number of interesting features including a flat band. We also study the finite temperature and finite chemical potential cases where the geometry is replaced by Lifshitz black hole solutions.

hep-th↗

arXiv2010

Chaos in Sandpile Models

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.

cond-mat.stat-mech↗