arXiv subjects

Arpan Bhattacharyya

Publications and source records attributed to Arpan Bhattacharyya.

At least 91 records · Page 5Linked to original sources

arXiv2019

Entanglement Entropy for $TT$ deformed CFT in general dimensions

We consider deformation of a generic $d$ dimensional ($d\geq 2$) large-$N$ CFT on a sphere by a spin-0 operator which is bilinear in the components of the stress tensor. Such a deformation has been proposed to be holographically dual to an $AdS_{d+1}$ bulk with a hard radial cut-off. We compute the exact partition function and find the entanglement entropy from the field theory side in various dimensions and compare with the corresponding holographic results. We also compute renormalized entanglement entropy both in field theory and holography and find complete agreement between them.

hep-th↗

arXiv2019

Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves

Cataclysmic astrophysical phenomena can produce impulsive gravitational waves that can possibly be detected by the advanced versions of present-day detectors in the future. Gluing of two spacetimes across a null surface produces impulsive gravitational waves (in the phraseology of Penrose [1]) having a Dirac Delta function type pulse profile along the surface. It is known that BMS-like symmetries appear as soldering freedom while we glue two spacetimes along a null surface. In this note, we study the effect of such impulsive gravitational waves on test particles (detectors) or geodesics. We show explicitly some measurable effects that depend on BMS-transformation parameters on timelike and null geodesics. BMS-like symmetry parameters carried by the gravitational wave leave some "memory" on test geodesics upon passing through them.

hep-th↗

arXiv2019

Universal Local Operator Quenches and Entanglement Entropy

We present a new class of local quenches described by mixed states, parameterized universally by two parameters. We compute the evolutions of entanglement entropy for both a holographic and Dirac fermion CFT in two dimensions. This turns out to be equivalent to calculations of two point functions on a torus. We find that in holographic CFTs, the results coincide with the known results of pure state local operator quenches. On the other hand, we obtain new behaviors in the Dirac fermion CFT, which are missing in the pure state counterpart. By combining our results with the inequalities known for von-Neumann entropy, we obtain an upper bound of the pure state local operator quenches in the Dirac fermion CFT. We also explore predictions about the behaviors of entanglement entropy for more general mixed states.

hep-th↗

arXiv2019

Investigations of the heterometallic Ludwigite Ni${_2}$AlBO${_5}$

We present magnetic, thermodynamic, dielectric and structural investigations on the aluminoborate Ni${_2}$AlBO${_5}$, belonging to the ludwigite family. Room temperature structural refinement suggests that the system crystallizes in the orthorhombic $Pbam$ symmetry, in similarity with most members of this material class. Magnetic and thermodynamic measurements shows that the system undergoes a phase transition to an antiferromagnetic state at 38K, signatures of which are also seen in the lattice parameters and the dielectric constant. Short range magnetic correlations appear to persist to much higher temperatures - a regime in which the ac susceptibility exhibits a power law temperature dependence, in agreement with that expected for random exchange Heisenberg antiferromagnetic spin chains.

cond-mat.str-el↗

arXiv2019

Entanglement of Purification in Many Body Systems and Symmetry Breaking

We study the entanglement of purification (EoP), a measure of total correlation between two subsystems $A$ and $B$, for free scalar field theory on a lattice and the transverse-field Ising model by numerical methods. In both of these models, we find that the EoP becomes a non-monotonic function of the distance between $A$ and $B$ when the total number of lattice sites is small. When it is large, the EoP becomes monotonic and shows a plateau-like behavior. Moreover, we show that the original reflection symmetry which exchanges $A$ and $B$ can get broken in optimally purified systems. In the Ising model, we find this symmetry breaking in the ferromagnetic phase. We provide an interpretation of our results in terms of the interplay between classical and quantum correlations.

hep-th↗

arXiv2019

Notes on the Causal Structure in a Tensor Network

In this paper we attempt to understand Lorentzian tensor networks, as a preparation for constructing tensor networks that can describe more exotic backgrounds such as black holes. To define notions of reference frames and switching of reference frames on a tensor network, we will borrow ideas from the algebraic quantum field theory literature. With these definitions, we construct simple examples of Lorentzian tensor networks and solve the spectrum for a choice of ``inertial frame'' based on Gaussian models of fermions and integrable models. In particular, the tensor network can be viewed as a periodically driven Floquet system, that by-pass the ``doubling problem'' and gives rise to fermions with exactly linear dispersion relations. We will find that a boost operator connecting different inertial frames, and notions of ``Rindler observers'' can be defined, and that important physics in Lorentz invariant QFT, such as the Unruh effect, can be captured by such skeleton of spacetime. We find interesting subtleties when the same approach is directly applied to bosons -- the operator algebra contains commutators that take the wrong sign -- resembling bosons behind horizons.

hep-th↗

arXiv2019

Time Evolution of Complexity: A Critique of Three Methods

In this work, we propose a testing procedure to distinguish between the different approaches for computing complexity. Our test does not require a direct comparison between the approaches and thus avoids the issue of choice of gates, basis, etc. The proposed testing procedure employs the information-theoretic measures Loschmidt echo and Fidelity; the idea is to investigate the sensitivity of the complexity (derived from the different approaches) to the evolution of states. We discover that only circuit complexity obtained directly from the wave function is sensitive to time evolution, leaving us to claim that it surpasses the other approaches. We also demonstrate that circuit complexity displays a universal behaviour---the complexity is proportional to the number of distinct Hamiltonian evolutions that act on a reference state. Due to this fact, for a given number of Hamiltonians, we can always find the combination of states that provides the maximum complexity; consequently, other combinations involving a smaller number of evolutions will have less than maximum complexity and, hence, will have resources. Finally, we explore the evolution of complexity in non-local theories; we demonstrate the growth of complexity is sustained over a longer period of time as compared to a local theory.

hep-th↗

arXiv2018

Robustness of Topological Order in the Toric Code with Open Boundaries

We analyze the robustness of topological order in the toric code in an open boundary setting in the presence of perturbations. The boundary conditions are introduced on a cylinder, and are classified into condensing and non-condensing classes depending on the behavior of the excitations at the boundary under perturbation. For the non-condensing class, we see that the topological order is more robust when compared to the case of periodic boundary conditions while in the condensing case topological order is lost as soon as the perturbation is turned on. In most cases, the robustness can be understood by the quantum phase diagram of a equivalent Ising model.

cond-mat.str-el↗

arXiv2018

Measurement independent magnetocaloric effect in Mn-rich Mn-Fe-Ni-Sn(Sb/In) Heusler alloys

We report a systematic study on the magneto-structural transition in Mn-rich Fe-doped Mn-Fe-Ni-Sn(Sb/In) Heusler alloys by keeping the total valence electron concentration (e/a ratio) fixed. The martensitic transition (MT) temperature is found to shift by following a proportional relationship with the e/a ratio of the magnetic elements alone. The magnetic entropy change across MT for a selected sample (Mn49FeNi40Sn9In) has been estimated from three different measurement methods (isofield magnetization (M) vs temperature (T), isothermal M vs field (H) and heat capacity (HC) vs T). We observed that though the peak value of magnetic entropy change changes with the measurement methods, the broadened shape of the magnetic entropy change vs T curves and the corresponding cooling power (~140 Jkg-1) remains invariant. The equivalent adiabatic temperature change ~ -2.6 K has been obtained from indirect measurements of temperature change. Moreover, an exchange bias field ~ 783 Oe at 5 K and a magnetoresistance of -30% are also obtained in one of these materials.

cond-mat.mtrl-sci↗

arXiv2018

Weak Ferromagnetism and Time-Stable Remanence in Hematite: Effect of Shape, Size and Morphology

We have recently established that a number of Dzyaloshinskii-Moriya interaction driven canted antiferromagnets or weak ferrromagnets (WFM) including hematite exhibit an ultra-slow magnetization relaxation phenomenon, leading to the observation of a time-stable remanence (Phys. Rev. B 96, 104422 (2017)). In this work, our endeavor is to optimize the magnitude of this time-stable remanence for the hematite crystallites, as a function of shape size and morphology. A substantial enhancement in the magnitude of this unique remanence is observed in porous hematite, consisting of ultra-small nano particles, as compared to crystallites grown in regular morphology, such as cuboids or hexagonal plates. This time-stable remanence exhibits a peak-like pattern with magnetic field, which is significantly sharper in porous sample. The extent and the magnitude of the spin canting associated with the WFM phase can be best gauged by the presence of this remanence and its unusual magnetic field dependence. Temperature variation of lattice parameters bring out correlations between strain effects that alter the bond length and bond angle associated with primary super exchange paths, which in-turn systematically alter the magnitude of the time-stable remanence. This study provides insights regarding a long standing problems of anomalies in the magnitude of magnetization on repeated cooling in case of hematite. Our data caps on these anomalies, which we argue, arise due to spontaneous spin canting associated with WFM phase. Our results also elucidate on why thermal cycling protocols during bulk magnetization measurements are even more crucial for hematite which exhibits both canted as well as pure antiferromgnetic phase.

cond-mat.str-el↗

arXiv2018

Probing analytical and numerical integrability: The curious case of $(AdS_5\times S^5)_η$

Motivated by recent studies related to integrability of string motion in various backgrounds via analytical and numerical procedures, we discuss these procedures for a well known integrable string background $(AdS_5\times S^5)_η$. We start by revisiting conclusions from earlier studies on string motion in $(\mathbb{R}\times S^3)_η$ and $(AdS_3)_η$ and then move on to more complex problems of $(\mathbb{R}\times S^5)_η$ and $(AdS_5)_η$. Discussing both analytically and numerically, we deduce that while $(AdS_5)_η$ strings do not encounter any irregular trajectories, string motion in the deformed five-sphere can indeed, quite surprisingly, run into chaotic trajectories. We discuss the implications of these results both on the procedures used and the background itself.

hep-th↗

arXiv2018

Soldering freedom and BMS-like transformations

When two spacetimes are stitched across a null-shell placed at the horizon of a black hole BMS-supertranslation like soldering freedom arises if one demands the induced metric on the horizon shell should remain invariant under the translations generated by the null generators of the shell. We revisit this phenomenon at the horizon of rotating shells and obtain BMS like symmetries. We further show that superrotation like soldering symmetries in the form of conformal isometries can emerge whenever the degenerate metric of any null hypersurface admits a dependency on null (degenerate direction) coordinate. This kind of conformal isometry can also appear for a null surface situated very close to the horizon of black holes. We also study the intrinsic properties of different kinds of horizon shells considered in this note.

hep-th↗

arXiv2018

Circuit complexity in interacting QFTs and RG flows

We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $ϕ^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory. Our approach uses Nielsen's geometric method, which translates into working out the geodesic equation arising from a certain cost functional. We present a general method, making use of integral transforms, to do the required lattice sums analytically and give explicit expressions for the $d=2,3$ cases. Our method enables a study of circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the $ϕ^4$ interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group.

hep-th↗

arXiv2018

Null hypersurface quantization, electromagnetic duality and asymptotic symmetries of Maxwell theory

In this paper we consider introducing careful regularization in the quantization of Maxwell theory in the asymptotic null infinity. This allows systematic discussions of the commutators in various boundary conditions, and application of Dirac brackets accordingly in a controlled manner. This method is most useful when we consider asymptotic charges that are not localized at the boundary $u\to \pm \infty$ like large gauge transformations. We show that our method reproduces the operator algebra in known cases, and it can be applied to other space-time symmetry charges such as the BMS transformations. We also obtain the asymptotic form of the U(1) charge following from the electromagnetic duality in an explicitly EM symmetric Schwarz-Sen type action. Using our regularization method, we demonstrate that the charge generates the expected transformation of a helicity operator. Our method promises applications in more generic theories.

hep-th↗

arXiv2018

Path-Integral Complexity for Perturbed CFTs

In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field theories as well as general arguments of RG flows in field theories. Our optimization is performed by minimizing the path-integral complexity functional that depends on the metric and also on the relevant couplings. Then, we compute the optimal metric perturbatively and find that it agrees with the time slice of the hyperbolic metric perturbed by a scalar field in the AdS/CFT correspondence. Last but not the least, we estimate contributions to complexity from relevant perturbations.

hep-th↗

arXiv2018

Entanglement of Purification in Free Scalar Field Theories

We compute the entanglement of purification (EoP) in a 2d free scalar field theory with various masses. This quantity measures correlations between two subsystems and is reduced to the entanglement entropy when the total system is pure. We obtain explicit numerical values by assuming minimal gaussian wave functionals for the purified states. We find that when the distance between the subsystems is large, the EoP behaves like the mutual information. However, when the distance is small, the EoP shows a characteristic behavior which qualitatively agrees with the conjectured holographic computation and which is different from that of the mutual information. We also study behaviors of mutual information in purified spaces and violations of monogamy/strong superadditivity.

hep-th↗

arXiv2018

Tensor network and ($p$-adic) AdS/CFT

We use the tensor network living on the Bruhat-Tits tree to give a concrete realization of the recently proposed $p$-adic AdS/CFT correspondence (a holographic duality based on the $p$-adic number field $\mathbb{Q}_p$). Instead of assuming the $p$-adic AdS/CFT correspondence, we show how important features of AdS/CFT such as the bulk operator reconstruction and the holographic computation of boundary correlators are automatically implemented in this tensor network.

hep-th↗

arXiv2018

Fast spinning strings on $ η$ deformed $ AdS_5 \times S^{5} $

In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over $ η$ deformed $ AdS_5 \times S^{5} $ in the so called fast spinning limit. In our analysis, we focus only on the bosonic part of the full superstring action and compute the relevant limits on both $(R \times S^{3})_η $ and $(R \times S^{5})_η $ models. The resulting system reveals that in the fast spinning limit, the sigma model on $ η$ deformed $S^5$ could be $\textit{approximately}$ thought of as the continuum limit of anisotropic $ SU(3) $ Heisenberg spin chain model. We compute the energy for a certain class of spinning strings in deformed $S^5$ and we show that this energy can be mapped to that of a similar spinning string in the purely imaginary $β$ deformed background.

hep-th↗