arXiv subjects

Arpan Bhattacharyya

Publications and source records attributed to Arpan Bhattacharyya.

At least 109 records · Page 6Linked to original sources

arXiv2018

Holographic Lifshitz fluids in 1+1 dimensions

In this paper, using the techniques of Gauge/gravity duality we explore the hydrodynamic regime of $ z=3 $ Lifshitz fixed points in $ 1+1 $ dimensions. The speed of sound in the non-relativistic plasma turns out to be $\sqrt{3}$, which clearly violates the conjectured upper bound. We identify this as a natural consequence of the Lorentz symmetry breakdown at $ z=3 $ Lifshitz fixed point. In our analysis, we compute bulk viscosity to entropy ratio for quantum field theory dual to Lifshitz gravity in $ 2+1$ dimensions and it turns out that for this particular holographic model this ratio is above the conjectured lower bound.

hep-th↗

arXiv2017

Instantons and Entanglement Entropy

We would like to put the area law -- believed to by obeyed by entanglement entropies in the ground state of a local field theory -- to scrutiny in the presence of non-perturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton effects are well understood, including $U(1)$ gauge theory in 2+1 dimensions and false vacuum decay in $ϕ^4$ theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.

hep-th↗

arXiv2017

Inspecting non-perturbative contributions to the Entanglement Entropy via wavefunctions

In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true ground state after taking the tunnelling effects into account and find some simple patterns. Notably, in the case of multiple particle interactions, entanglement entropy generically decreases with increasing number of minima. The knowledge of the subsystem actually increases with the number of minima. The reduced density matrix can also be seen to have close connections with graph spectra. In a more careful study of the two-well tunnelling system, we also extract the exponentially suppressed tail contribution, the analogues of instantons. To understand the effects of multiple minima in a field theory, it inspires us to inspect wavefunctions in a toy model of bosonic field describing quasi-particles of two different condensates related by Bogoliubov transformations. We find that the area law is naturally preserved. This is probably a useful set of perspectives that promise wider applications.

hep-th↗

arXiv2017

Quasi Static Remanence in Dzyaloshinskii-Moriya Interaction driven Weak Ferromagnets and Piezomagnets

We explore remanent magnetization ($μ$) as a function of time and temperature, in a variety of rhombohedral antiferromagnets (AFM) which are also weak ferromagnets (WFM) and piezomagnets (PzM). These measurements, across samples with length scales ranging from nano to bulk, firmly establish the presence of a remanence that is quasi static in nature and exhibits a counter-intuitive magnetic field dependence. These observations unravel an ultra-slow magnetization relaxation phenomenon related to this quasi static remanence. This feature is also observed in a defect free single crystal of $α$-Fe$_2$O$_3$, which is a canonical WFM and PzM. Notably, $α$-Fe$_2$O$_3$ is not a typical geometrically frustrated AFM and in single crystal form, it is also devoid of any size or interface effects, which are the usual suspects for a slow magnetization relaxation phenomenon. The underlying pinning mechanism appears exclusive to those AFM which are either symmetry allowed WFM, driven by Dzyaloshinskii-Moriya Interaction (DMI) or can generate this trait by tuning of size and interface. The qualitative features of the quasi static remanence indicate that such WFM are potential piezomagnets, in which magnetization can be tuned by \textit{stress} alone.

cond-mat.str-el↗

arXiv2017

Thermodynamics of local baths in the context of work extraction

We consider locally thermal states (for two qubits) with certain amount of quantum entanglement present between them. Unlike previous protocols we show how work can be extracted by performing local unitary operations on this state by allowing those two qubits to interact with thermal baths of different temperatures, thereby gradually removing the entanglement between them till they reach a direct product state. Also we demonstrate that, further work can be extracted from this direct product state by performing global unitary operation, thereby establishing that work can be extracted from a system composed of locally thermal subsystems even after removing quantum correlations between them if the subsystems are thermalized at different temperatures. Also we show that even if we consider a initial state where there is no entanglement between the two qubits, we can also extract work locally using our method.

quant-ph↗

arXiv2016

A reentrant superspin glass state and magnetization steps in the oxyborate Co2AlBO5

An oxyborate Co2AlBO5 belonging to the ludwigite family is investigated using structural, thermodynamic, dielectric and magnetic measurements. Magnetic measurements indicate that this system is seen to exhibit long range magnetic ordering at T{_N} = 42 K, signatures of which are also seen in the specific heat, dielectric susceptibility, and the lattice parameters. The absence of a structural phase transition down to the lowest measured temperatures, distinguishes it from the more extensively investigated Fe-based ludwigites. At low temperatures, the system is seen to stabilize in a reentrant superspin glass phase at T{_G} = 10.6 K from within the magnetically ordered state. This ground state is also characterized by magnetic field induced metamagnetic transitions, which at the lowest measured temperatures exhibit a number of sharp magnetization steps, reminiscent of that observed in the mixed valent manganites.

cond-mat.str-el↗

arXiv2016

Exploring the Tensor Networks/AdS Correspondence

In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

hep-th↗

arXiv2016

Relative Entropy, Mixed Gauge-Gravitational Anomaly and Causality

In this note we explored the holographic relative entropy in the presence of the 5d Chern-Simons term, which introduces a mixed gauge-gravity anomaly to the dual CFT. The theory trivially satisfies an entanglement first law. However, to quadratic order in perturbations of the stress tensor $T$ and current density $J$, there is a mixed contribution to the relative entropy bi-linear in $T$ and $J$, signalling a potential violation of the positivity of the relative entropy. Miraculously, the term vanishes up to linear order in a derivative expansion. This prompted a closer inspection on a different consistency check, that involves time-delay of a graviton propagating in a charged background, scattered via a coupling supplied by the Chern-Simons term. The analysis suggests that the time-delay can take either sign, potentially violating causality for any finite value of the CS coupling.

hep-th↗

arXiv2016

Entropy functionals and c-theorems from the second law

We show that for a general four derivative theory of gravity, only the holographic entanglement entropy functionals obey the second law at linearized order in perturbations. We also derive bounds on the higher curvature couplings in several examples, demanding the validity of the second law for higher order perturbations. For the five dimensional Gauss-Bonnet theory in the context of AdS/CFT, the bound arising from black branes coincides with there being no sound channel instability close to the horizon. Repeating the analysis for topological black holes, the bound coincides with the tensor channel causality constraint (which is responsible for the viscosity bound). Furthermore, we show how to recover the holographic c-theorems in higher curvature theories from similar considerations based on the Raychaudhuri equation.

hep-th↗

arXiv2015

RG Flow and Thermodynamics of Causal Horizons in Higher-Derivative AdS Gravity

In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary $c$-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in arXiv:1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.

hep-th↗

arXiv2015

Viscosity bound for anisotropic superfluids in higher derivative gravity

In the present paper, based on the principles of gauge/gravity duality we analytically compute the shear viscosity to entropy ratio corresponding to the superfluid phase in Einstein Gauss-Bonnet gravity. From our analysis we note that the ratio indeed receives a finite temperature correction below certain critical temperature. This proves the non universality of shear viscosity to entropy ratio in higher derivative theories of gravity. We also compute the upper bound for the Gauss-Bonnet coupling corresponding to the symmetry broken phase and note that the upper bound on the coupling does not seem to change as long as we are close to the critical point of the phase diagram. However the corresponding lower bound of the shear viscosity to entropy ratio seems to get modified due to the finite temperature effects.

hep-th↗

arXiv2015

Renormalized Entanglement Entropy for BPS Black Branes

We compute the renormalized entanglement entropy (REE) for BPS black solutions in ${\cal N}=2$, 4d gauged supergravity. We find that this quantity decreases monotonically with the size of the entangling region until it reaches a critical point, then increases and approaches the entropy density of the brane. This behavior can be understood as a consequence of the REE being driven by two competing factors, namely entanglement and the mixedness of the black brane. In the UV entanglement dominates, whereas in the IR the mixedness takes over.

hep-th↗

arXiv2014

On entanglement entropy functionals in higher derivative gravity theories

In arXiv:1310.5713 and arXiv:1310.6659 a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the four-derivative case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.

hep-th↗

arXiv2014

Attractive holographic $c$-functions

Using the attractor mechanism for extremal solutions in ${\cal N}=2$ gauged supergravity, we construct a $c$-function that interpolates between the central charges of theories at ultraviolet and infrared conformal fixed points corresponding to anti-de Sitter geometries. The $c$-function we obtain is couched purely in terms of bulk quantities and connects two different dimensional CFTs at the stable conformal fixed points under the RG flow.

hep-th↗

arXiv2014

Constraining gravity using entanglement in AdS/CFT

We investigate constraints imposed by entanglement on gravity in the context of holography. First, by demanding that relative entropy is positive and using the Ryu-Takayanagi entropy functional, we find certain constraints at a nonlinear level for the dual gravity. Second, by considering Gauss-Bonnet gravity, we show that for a class of small perturbations around the vacuum state, the positivity of the two point function of the field theory stress tensor guarantees the positivity of the relative entropy. Further, if we impose that the entangling surface closes off smoothly in the bulk interior, we find restrictions on the coupling constant in Gauss-Bonnet gravity. We also give an example of an anisotropic excited state in an unstable phase with broken conformal invariance which leads to a negative relative entropy.

hep-th↗

arXiv2013

On generalized gravitational entropy, squashed cones and holography

We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.

hep-th↗

arXiv2013

Entanglement entropy from the holographic stress tensor

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero the time-time component of the Brown-York stress tensor evaluated on the co-dimension one entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription.

hep-th↗

arXiv2013

Entanglement entropy from surface terms in general relativity

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighbourhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1 dimensional CFTs at finite temperature whose gravity dual is the BTZ black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

gr-qc↗