arXiv subjects

Ipsita Mandal

Publications and source records attributed to Ipsita Mandal.

106 records · Page 6Linked to original sources

arXiv2016

Exceptional point description of one-dimensional chiral topological superconductors/superfluids in BDI class

We show that certain singularities of the Hamiltonian in the complex wave vector space can be used to identify topological quantum phase transitions for $1D$ chiral topological superconductors/superfluids in the BDI class. These singularities fall into the category of the so-called exceptional points ($EP$'s) studied in the context of non-Hermitian Hamiltonians describing open quantum systems. We also propose a generic formula in terms of the properties of the $EP$'s to quantify the exact number of Majorana zero modes in a particular chiral topological superconducting phase, given the values of the parameters appearing in the Hamiltonian. This formula serves as an alternative to the familiar integer ($\mathbb{Z}$) winding number invariant characterizing topological superconductor/superfluid phases in the chiral BDI class.

cond-mat.mes-hall↗

arXiv2016

Super-GCA from $\mathcal{N} = (2,2)$ Super-Virasoro

We derive the extended Supersymmetric Galilean Conformal Algebra (SGCA) in two spacetime dimensions by the method of group contraction on $2d$ $\mathcal{N}=(2,2)$ superconformal algebra. Both the parent and daughter algebras are infinite-dimensional. We provide the representation theory of the algebra. We adopt a superspace formalism for the SGCA fields, allowing us to write them down in a compact notation as components of superfields. We also discuss correlation functions, short supermultiplets and null states.

hep-th↗

arXiv2014

Pairing in half-filled Landau level

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current-current interactions. Our results show that there can be a \emph{continuous} transition from the Halperin-Lee-Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that $\ell=1$ angular momentum channel is quite different from higher angular momenta $\ell\ge 3$. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction $ν=\frac{1}{2}+\frac{1}{2}$ is quantitatively changed from the previously established results but not qualitatively.

cond-mat.str-el↗

arXiv2013

Amplitude mode of the $d$-density wave state and its relevance to high-$T_c$ cuprates

We calculate the spectrum of the amplitude mode, the analog of the Higgs mode in high energy physics, for the $d$-density wave (DDW) state proposed to describe the pseudogap phase of the high $T_c$ cuprates. Even though the state breaks translational symmetry by a lattice spacing and is described by a particle-hole singlet order parameter at the wave vector $q=Q=(π,π)$, remarkably, we find that the amplitude mode spectrum can have peaks at both $q=(0,0)$ and $q=Q=(π,π)$; we shall lattice spacing to unity. In general, the spectrum is non-universal, and, depending on the microscopic parameters, can have one or two peaks in the Brillouin zone, signifying existence of two kinds of magnetic excitations. Our theory sheds important light on how multiple inelastic neutron peaks at different wave vectors can, in principle, arise even with an order parameter that condenses at $Q=(π,π)$.

cond-mat.supr-con↗

arXiv2013

Higher angular momentum pairing from transverse gauge interactions

In this paper, we study superconductivity of nonrelativistic fermions at finite-density coupled to a transverse $U(1)$ gauge field, with the effective interaction including the Landau-damping. This model, first studied by Holstein, Norton, and Pincus [Phys. Rev B, {\bf 8}, 2649 (1973)] has been known as an example of a non-Fermi liquid, {ı.e.} a metallic state in which the decay rate of a quasiparticle is large compared to the characteristic quasiparticle energy; other examples of the non-Fermi liquid includes the 2d electron gas in a magnetic field at $ν=1/2$ and the normal state of optimally doped cuprate superconductors. Our study thus addresses the question of whether or not non-Fermi liquids, like Fermi liquids, are unstable towards the formation of superconductivity.The results are (i) the non-Fermi liquid is stable against superconductivity below a critical gauge coupling, (ii) above this critical coupling, the ground state is an unconventional superconductor with angular momentum $\ell \ge 2$. Our results are obtained from a solution of the Dyson-Nambu equation. Note that in this problem there is a quantum critical point between a non-Fermi liquid state and the superconducting state, as the critical coupling is nonzero. This is in contrast to a weakly coupled metal, which exhibits superconductivity for infinitesimally weak interaction regardless of its sign.

cond-mat.str-el↗

arXiv2012

Black Hole Microstate Counting and its Macroscopic Counterpart

We survey recent results on the exact dyon spectrum in a class of N=4 supersymmetric string theories, and discuss how the results can be understood from the macroscopic viewpoint using AdS_2/CFT_1 correspondence. The comparison between the microscopic and the macroscopic results includes power suppressed corrections to the entropy, the sign of the index, logarithmic corrections and also the twisted index measuring the distribution of discrete quantum numbers among the microstates.

hep-th↗

arXiv2012

Majorana zero modes in a quantum Ising chain with longer-ranged interactions

A one-dimensional Ising model in a transverse field can be mapped onto a system of spinless fermions with p-wave superconductivity. In the weak-coupling BCS regime, it exhibits a zero energy Majorana mode at each end of the chain. Here, we consider a variation of the model, which represents a superconductor with longer ranged kinetic energy and pairing amplitudes, as is likely to occur in more realistic systems. It possesses a richer zero temperature phase diagram and has several quantum phase transitions. From an exact solution of the model these phases can be classified according to the number of Majorana zero modes of an open chain: 0, 1, or 2 at each end. The model posseses a multicritical point where phases with 0, 1, and 2 Majorana end modes meet. The number of Majorana modes at each end of the chain is identical to the topological winding number of the Anderson's pseudospin vector that describes the BCS Hamiltonian. The topological classification of the phases requires a unitary time-reversal symmetry to be present. When this symmetry is broken, only the number of Majorana end modes modulo 2 can be used to distinguish two phases. In one of the regimes, the wave functions of the two phase shifted Majorana zero modes decays exponentially in space but but in an oscillatory manner. The wavelength of oscillation is identical to the asymptotic connected spin-spin correlation of the XY-model in a transverse field to which our model is dual.

cond-mat.str-el↗

arXiv2011

Logarithmic Corrections to N=4 and N=8 Black Hole Entropy: A One Loop Test of Quantum Gravity

We compute logarithmic corrections to the entropy of supersymmetric extremal black holes in N=4 and N=8 supersymmetric string theories and find results in perfect agreement with the microscopic results. In particular these logarithmic corrections vanish for quarter BPS black holes in N=4 supersymmetric theories, but has a finite coefficient for 1/8 BPS black holes in the N=8 supersymmetric theory. On the macroscopic side these computations require evaluating the one loop determinant of massless fields around the near horizon geometry, and include, in particular, contributions from dynamical four dimensional gravitons propagating in the loop. Thus our analysis provides a test of one loop quantum gravity corrections to the black hole entropy, or equivalently of the AdS_2/CFT_1 correspondence. We also extend our analysis to N=2 supersymmetric STU model and make a prediction for the logarithmic correction to the black hole entropy in that theory.

hep-th↗

arXiv2010

Supersymmetric Extension of GCA in 2d

We derive the infinite dimensional Supersymmetric Galilean Conformal Algebra (SGCA) in the case of two spacetime dimensions by performing group contraction on 2d superconformal algebra. We also obtain the representations of the generators in terms of superspace coordinates. Here we find realisations of the SGCA by considering scaling limits of certain 2d SCFTs which are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We focus on the Neveu-Schwarz sector of the parent SCFTs and develop, in parallel to the GCA studies recently in (arXiv:0912.1090), the representation theory based on SGCA primaries, Ward identities for their correlation functions and their descendants which are null states.

hep-th↗

arXiv2010

GCA in 2d

We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2d. Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2d CFT, many of the tools for the analysis of the quantum mechanical GCA. These include the representation theory based on GCA primaries, Ward identities for their correlation functions and a nonrelativistic Kac table. In particular, the null vectors of the GCA lead to differential equations for the four point function. The solution to these equations in the simplest case is explicitly obtained and checked to be consistent with various requirements.

hep-th↗

arXiv2009

On Representations and Correlation Functions of Galilean Conformal Algebras

Galilean Conformal Algebras (GCA) have been recently proposed as a different non-relativistic limit of the AdS/CFT conjecture. In this note, we look at the representations of the GCA. We also construct explicitly the two and three point correlators in this non-relativistic limit of CFT and comment on the differences with the relativistic case and also the more studied Schrodinger group.

hep-th↗

arXiv2009

Supersymmetry, Localization and Quantum Entropy Function

AdS_2/CFT_1 correspondence leads to a prescription for computing the degeneracy of black hole states in terms of path integral over string fields living on the near horizon geometry of the black hole. In this paper we make use of the enhanced supersymmetries of the near horizon geometry and localization techniques to argue that the path integral receives contribution only from a special class of string field configurations which are invariant under a subgroup of the supersymmetry transformations. We identify saddle points which are invariant under this subgroup. We also use our analysis to show that the integration over infinite number of zero modes generated by the asymptotic symmetries of AdS_2 generate a finite contribution to the path integral.

hep-th↗

arXiv2009

Black Hole Hair Removal

Macroscopic entropy of an extremal black hole is expected to be determined completely by its near horizon geometry. Thus two black holes with identical near horizon geometries should have identical macroscopic entropy, and the expected equality between macroscopic and microscopic entropies will then imply that they have identical degeneracies of microstates. An apparent counterexample is provided by the 4D-5D lift relating BMPV black hole to a four dimensional black hole. The two black holes have identical near horizon geometries but different microscopic spectrum. We suggest that this discrepancy can be accounted for by black hole hair, -- degrees of freedom living outside the horizon and contributing to the degeneracies. We identify these degrees of freedom for both the four and the five dimensional black holes and show that after their contributions are removed from the microscopic degeneracies of the respective systems, the result for the four and five dimensional black holes match exactly.

hep-th↗

arXiv2009

Supersymmetric Extension of Galilean Conformal Algebras

The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field theory. In this paper, we extend the analysis to include supersymmetry. We work at the level of the co-ordinates in superspace to construct the N=1 Super Galilean conformal algebra. One of the interesting outcomes of the analysis is that one is able to naturally extend the finite algebra to an infinite one. This looks structurally similar to the N=1 superconformal algebra in two dimensions, but is different. We also comment on the extension of our construction to cases of higher $N$.

hep-th↗

arXiv2008

Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions

We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdS_{d+1} long wavelength solutions of Einstein's equations with a negative cosmological constant, for all d>2. We find simple explicit expressions for the stress tensor (slightly generalizing the recent result by Haack and Yarom (arXiv:0806.4602)), the full dual bulk metric and an entropy current of this strongly coupled conformal fluid, to second order in the derivative expansion, for arbitrary d>2. We also rewrite the well known exact solutions for rotating black holes in AdS_{d+1} space in a manifestly fluid dynamical form, generalizing earlier work in d=4. To second order in the derivative expansion, this metric agrees with our general construction of the metric dual to fluid flows.

hep-th↗

arXiv2007

Critical properties of spherically symmetric black hole accretion in Schwarzschild geometry

The stationary spherically symmetric accretion flow in the Schwarzschild metric has been set up as an autonomous first-order dynamical system, and it has been studied completely analytically. Of the three possible critical points in the flow, the one that is physically realistic behaves like the saddle point of the standard Bondi accretion problem. One of the two remaining critical points exhibits the strange mathematical behaviour of being either a saddle point or a centre-type point, depending on the values of the flow parameters. The third critical point is always unphysical and behaves like a centre-type point. The treatment has been extended to pseudo-Schwarzschild flows for comparison with the general relativistic analysis.

astro-ph↗