arXiv subjects

M. Reza Mohammadi Mozaffar

Publications and source records attributed to M. Reza Mohammadi Mozaffar.

32 records · Page 2Linked to original sources

arXiv2018

Renormalization Group Circuits for Weakly Interacting Continuum Field Theories

We develop techniques to systematically construct local unitaries which map scale-invariant, product state wavefunctionals to the ground states of weakly interacting, continuum quantum field theories. More broadly, we devise a "quantum circuit perturbation theory" to construct local unitaries which map between any pair of wavefunctionals which are each Gaussian with arbitrary perturbative corrections. Further, we generalize cMERA to interacting continuum field theories, which requires reworking the existing formalism which is tailored to non-interacting examples. Our methods enable the systematic perturbative calculation of cMERA circuits for weakly interacting theories, and as a demonstration we compute the 1-loop cMERA circuit for scalar $φ^4$ theory and analyze its properties. In this case, we show that Wilsonian renormalization of the spatial momentum modes is equivalent to a local position space cMERA circuit. This example provides new insights into the connection between position space and momentum space renormalization group methods in quantum field theory. The form of cMERA circuits derived from perturbation theory suggests useful ansatzes for numerical variational calculations.

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arXiv2018

Entanglement Renormalization for Weakly Interacting Fields

We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum. A key tool is "quantum circuit perturbation theory," which enables us to systematically construct unitaries that map between wavefunctionals which are Gaussian with arbitrary perturbative corrections. As an application, we construct a local, continuous MERA (cMERA) circuit that maps an unentangled scale-invariant state to the ground state of $φ^4$ theory to 1-loop. Our local cMERA circuit corresponds exactly to 1-loop Wilsonian RG on the spatial momentum modes. In other words, we establish that perturbative Wilsonian RG on spatial momentum modes can be equivalently recast as a local cMERA circuit in $φ^4$ theory, and argue that this correspondence holds more generally. Our analysis also suggests useful numerical ansatzes for cMERA in the non-perturbative regime.

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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.

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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.

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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.

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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.

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arXiv2015

On the Time Evolution of Holographic n-partite Information

We study various scaling behaviors of n-partite information during a process of thermalization after a global quantum quench for n disjoint system consisting of n parallel strips whose widths are much larger than the separation between them. By making use of the holographic description for entanglement entropy we explore holographic description of the n-partite information by which we show that it has a definite sign: it is positive for even n and negative for odd n. This might be thought of as an intrinsic property of a field theory which has gravity dual.

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arXiv2014

Thermalization in backgrounds with hyperscaling violating factor

We present an analytic solution of a Vaidya-charged black hole with a hyperscaling violating factor in an Einstein-Maxwell-dilaton model, where the scalar potential plays a key role in the existence of the solution. By making use of this result, we study the process of thermalization after a global quench in a theory which its gravitational description is provided by the resultant solution in the case of zero charge. In particular, we probe the system by entanglement entropy and show that it exhibits certain scaling behaviors during the process.

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arXiv2014

Entanglement Entropy for Logarithmic Conformal Field Theory

We study holographic entanglement entropy for certain logarithmic conformal field theories by making use of their gravity descriptions. The corresponding gravity descriptions are provided by higher derivative gravity at critical points where the equations of motion degenerate leading to a log gravity. When the central charge of the dual theory is zero, the entanglement entropy has a new divergent term whose coefficient is given by the new anomaly of the logarithmic conformal field theory.

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arXiv2014

Holographic Entanglement Entropy for 4D Conformal Gravity

Using the proposal for holographic entanglement entropy in higher derivative gravities, we compute holographic entanglement entropy for the conformal gravity in four dimensions which turns out to be finite. However, if one subtracts the contribution of the four dimensional Gauss-Bonnet term, the corresponding entanglement entropy has a divergent term and indeed restricted to an Einstein solution of the conformal gravity, the resultant entanglement entropy is exactly the same as that in the Einstein gravity. We will also make a comment on the first law of the entanglement thermodynamics for the conformal gravity in four dimensions.

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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.

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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.

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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.

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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.

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