arXiv subjects

Sumit R. Das

Publications and source records attributed to Sumit R. Das.

At least 37 records · Page 2Linked to original sources

arXiv2017

Universality in fast quantum quenches

We expand on the investigation of the universal scaling properties in the early time behaviour of fast but smooth quantum quenches in a general $d$-dimensional conformal field theory deformed by a relevant operator of dimension $Δ$ with a time-dependent coupling. The quench consists of changing the coupling from an initial constant value $λ_1$ by an amount of the order of $δλ$ to some other final value $λ_2$, over a time scale $δt$. In the fast quench limit where $δt$ is smaller than all other length scales in the problem, $ δt \ll λ_1^{1/(Δ-d)}, λ_2^{1/(Δ-d)}, δλ^{1/(Δ-d)}$, the energy (density) injected into the system scales as $δ{\cal E} \sim (δλ)^2 (δt)^{d-2Δ}$. Similarly, the change in the expectation value of the quenched operator at times earlier than the endpoint of the quench scales as $<{\cal O}_Δ> \sim δλ(δt)^{d-2Δ}$, with further logarithmic enhancements in certain cases. While these results were first found in holographic studies, we recently demonstrated that precisely the same scaling appears in fast mass quenches of free scalar and free fermionic field theories. As we describe in detail, the universal scaling refers to renormalized quantities, in which the UV divergent pieces are consistently renormalized away by subtracting counterterms derived with an adiabatic expansion. We argue that this scaling law is a property of the conformal field theory at the UV fixed point, valid for arbitrary relevant deformations and insensitive to the details of the quench protocol. Our results highlight the difference between smooth fast quenches and instantaneous quenches where the Hamiltonian abruptly changes at some time.

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arXiv2017

Universal scaling in fast quantum quenches in conformal field theories

We study the time evolution of a conformal field theory deformed by a relevant operator under a smooth but fast quantum quench which brings it to the conformal point. We argue that when the quench time scale $δt$ is small compared to the scale set by the relevant coupling, the expectation value of the quenched operator scales universally as $δg/ δt ^{2Δ-d}$ where $δg$ is the quench amplitude. This growth is further enhanced by a logarithmic factor in even dimensions. We present explicit results for free scalar and fermionic field theories, supported by an analytic understanding of the leading contribution for fast quenches. Results from this Letter suggest that this scaling result, first found in holography, is in fact universal to quantum quenches. Our considerations also show that this limit of fast smooth quenches is quite different from an instantaneous quench from one time-independent Hamiltonian to another, where the Schrodinger picture state at the time of the quench simply serves as an initial condition for subsequent evolution with the final Hamiltonian.

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arXiv2017

An exactly solvable quench protocol for integrable spin models

Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field Ising model on a one-dimensional chain and the Kitaev model on a two-dimensional honeycomb lattice using a nonlinear quench protocol which allows for exact analytical solutions of the dynamics. Our quench protocol starts with a finite mass gap at early times and crosses a critical point or a critical region, and we study the behaviour of one point functions of the quenched operator at the critical point or in the critical region as a function of the quench rate. For quench rates slow compared to the initial mass gap, we find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to the mass gap, but slow compared to the inverse lattice spacing, we find scaling behaviour similar to smooth fast continuum quenches. For quench rates of the same order of the lattice scale, the one point function saturates as a function of the rate, approaching the results of an abrupt quench. The presence of an extended critical surface in the Kitaev model leads to a variety of scaling exponents depending on the starting point and on the time where the operator is measured. We discuss the role of the amplitude of the quench in determining the extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the saturation.

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arXiv2017

Holographic entanglement entropy of a $1+1$ dimensional $p$-wave superconductor

We examine the behavior of entanglement entropy of a subsystem $A$ in a fully backreacted holographic model of a $1+1$ dimensional $p$ wave superconductor across the phase transition. For a given temperature, the system goes to a superconducting phase beyond a critical value of the charge density. The entanglement entropy, considered as a function of the charge density at a given temperature, has a cusp at the critical point. In addition, we find that there are three different behaviors in the condensed phase, depending on the subsystem size. For a subsystem size $l$ smaller than a critical size $l_{c1}$, entanglement entropy continues to increase as a function of the charge density as we cross the phase transition. When $l$ lies between $l_{c1}$ and another critical size $l_{c2}$ the entanglement entropy displays a non-monotonic behavior, while for $l > l_{c2}$ it decreases monotonically. At large charge densities entanglement entropy appears to saturate. The non-monotonic behavior leads to a novel phase diagram for this system.

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arXiv2017

Quantum Quenches in Free Field Theory: Universal Scaling at Any Rate

Quantum quenches display universal scaling in several regimes. For quenches which start from a gapped phase and cross a critical point, with a rate slow compared to the initial gap, many systems obey Kibble-Zurek scaling. More recently, a different scaling behaviour has been shown to occur when the quench rate is fast compared to all other physical scales, but still slow compared to the UV cutoff. We investigate the passage from fast to slow quenches in scalar and fermionic free field theories with time dependent masses for which the dynamics can be solved exactly for all quench rates. We find that renormalized one point functions smoothly cross over between the regimes.

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arXiv2017

Quantum Quench and Scaling of Entanglement Entropy

Global quantum quench with a finite quench rate which crosses critical points is known to lead to universal scaling of correlation functions as functions of the quench rate. In this work, we explore scaling properties of the entanglement entropy of a subsystem in a harmonic chain during a mass quench which asymptotes to finite constant values at early and late times and for which the dynamics is exactly solvable. When the initial state is the ground state, we find that for large enough subsystem sizes the entanglement entropy becomes independent of size. This is consistent with Kibble-Zurek scaling for slow quenches, and with recently discussed "fast quench scaling" for quenches fast compared to physical scales, but slow compared to UV cutoff scales.

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arXiv2017

Three Dimensional View of the SYK/AdS Duality

We show that the spectrum of the SYK model can be interpreted as that of a 3D scalar coupled to gravity. The scalar has a mass which is at the Breitenholer-Freedman bound of AdS$_2$, and subject to a delta function potential at the center of the interval along the third direction. This, through Kaluza-Klein procedure on AdS$_2 \times (S^1)/Z_2$, generates the spectrum reproducing the bi-local propagator at strong coupling. Furthermore, the leading $1/J$ correction calculated in this picture reproduces the known correction to the poles of the SYK propagator, providing credence to a conjecture that the bulk dual of this model can be interpreted as a three dimensional theory.

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arXiv2016

Old and New Scaling Laws in Quantum Quench

The response of a many body system to a time dependent coupling which passes through or approaches a critical point displays universal scaling behavior. In some regimes, scaling laws have been known since the 1970's. Recently holographic techniques have been used to understand the origins of such scaling. Along the way, new scaling behaviors in other regimes have been found in holographic models, which have later been shown to hold in a generic field theory regardless of holography. This contribution summarizes recent work on these various scaling regimes.

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arXiv2016

Fluctuations in a Cosmology with a Space-Like Singularity and their Gauge Theory Dual Description

We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a cosmological "singularity" - a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled region near the boundary, we reconstruct the bulk fluctuations after the singularity crossing making use of generic properties of boundary-to-bulk propagators. Finally, we extract the spectrum of the fluctuations at late times given some initial spectrum. We find that the spectral index is unchanged, but the amplitude increases due to the squeezing of the fluctuations during the course of the evolution. This investigation can teach us important lessons on how the spectrum of cosmological perturbations passes through a bounce which is singular from the bulk point of view but which is resolved using an ultraviolet complete theory of quantum gravity.

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arXiv2015

Smooth and fast versus instantaneous quenches in quantum field theory

We examine in detail the relationship between smooth fast quantum quenches, characterized by a time scale $δt$, and {\em instantaneous quenches}, within the framework of exactly solvable mass quenches in free scalar field theory. Our earlier studies \cite{dgm1,dgm2} highlighted that the two protocols remain distinct in the limit $δt \rightarrow 0$ because of the relation of the quench rate to the UV cut-off, i.e., $1/δt\llΛ$ always holds in the fast smooth quenches while $1/δt\simΛ$ for instantaneous quenches. Here we study UV finite quantities like correlators at finite spatial distances and the excess energy produced above the final ground state energy. We show that at late times and large distances (compared to the quench time scale) the smooth quench correlator approaches that for the instantaneous quench. At early times, we find that for small spatial separation and small $δt$, the correlator scales universally with $δt$, exactly as in the scaling of renormalized one point functions found in earlier work. At larger separation, the dependence on $δt$ drops out. The excess energy density is finite (for finite $mδt$) and scales in a universal fashion for all $d$. However, the scaling behaviour produces a divergent result in the limit $mδt \rightarrow 0$ for $d\ge4$, just as in an instantaneous quench, where it is UV divergent for $d \geq 4$. We argue that similar results hold for arbitrary interacting theories: the excess energy density produced is expected to diverge for scaling dimensions $Δ> d/2$.

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arXiv2015

Kibble-Zurek Scaling in Holographic Quantum Quench : Backreaction

We study gauge and gravity backreaction in a holographic model of quantum quench across a superfluid critical transition. The model involves a complex scalar field coupled to a gauge and gravity field in the bulk. In earlier work (arXiv:1211.1776) the scalar field had a strong self-coupling, in which case the backreaction on both the metric and the gauge field can be ignored. In this approximation, it was shown that when a time dependent source for the order parameter drives the system across the critical point at a rate slow compared to the initial gap, the dynamics in the critical region is dominated by a zero mode of the bulk scalar, leading to a Kibble-Zurek type scaling function. We show that this mechanism for emergence of scaling behavior continues to hold without any self-coupling in the presence of backreaction of gauge field and gravity. Even though there are no zero modes for the metric and the gauge field, the scalar dynamics induces adiabaticity breakdown leading to scaling. This yields scaling behavior for the time dependence of the charge density and energy momentum tensor.

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arXiv2014

dS/CFT at uniform energy density and a de Sitter "bluewall"

We describe a class of spacetimes that are asymptotically de Sitter in the Poincare slicing. Assuming that a dS/CFT correspondence exists, we argue that these are gravity duals to a CFT on a circle leading to uniform energy-momentum density, and are equivalent to an analytic continuation of the Euclidean AdS black brane. These are solutions with a complex parameter which then gives a real energy-momentum density. We also discuss a related solution with the parameter continued to a real number, which we refer to as a de Sitter "bluewall". This spacetime has two asymptotic de Sitter universes and Cauchy horizons cloaking timelike singularities. We argue that the Cauchy horizons give rise to a blue-shift instability.

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arXiv2013

Quantum Quench and Double Trace Couplings

We consider quantum quench by a time dependent double trace coupling in a strongly coupled large N field theory which has a gravity dual via the AdS/CFT correspondence. The bulk theory contains a self coupled neutral scalar field coupled to gravity with negative cosmological constant. We study the scalar dynamics in the probe approximation in two backgrounds: AdS soliton and AdS black brane. In either case we find that in equilibrium there is a critical phase transition at a {\em negative} value of the double trace coupling $κ$ below which the scalar condenses. For a slowly varying homogeneous time dependent coupling crossing the critical point, we show that the dynamics in the critical region is dominated by a single mode of the bulk field. This mode satisfies a Landau-Ginsburg equation with a time dependent mass, and leads to Kibble Zurek type scaling behavior. For the AdS soliton the system is non-dissipative and has $z=1$, while for the black brane one has dissipative $z=2$ dynamics. We also discuss the features of a holographic model which would describe the non-equilibrium dynamics around quantum critical points with arbitrary dynamical critical exponent $z$ and correlation length exponent $ν$. These analytical results are supported by direct numerical solutions.

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arXiv2013

Double Trace Flows and Holographic RG in dS/CFT correspondence

If there is a dS/CFT correspondence, time evolution in the bulk should translate to RG flows in the dual euclidean field theory. Consequently, although the dual field is expected to be non-unitary, its RG flows will carry an imprint of the unitary time evolution in the bulk. In this note we examine the prediction of holographic RG in de Sitter space for the flow of double and triple trace couplings in any proposed dual. We show quite generally that the correct form of the field theory beta functions for the double trace couplings is obtained from holography, provided one identifies the scale of the field theory with (i|T|) where T is the `time' in conformal coordinates. For dS(4), we find that with an appropriate choice of operator normalization, it is possible to have real n-point correlation functions as well as beta functions with real coefficients. This choice leads to an RG flow with an IR fixed point at negative coupling unlike in a unitary theory where the IR fixed point is at positive coupling. The proposed correspondence of Sp(N) vector models with de Sitter Vasiliev gravity provides a specific example of such a phenomenon. For dS(d+1) with even d, however, we find that no choice of operator normalization exists which ensures reality of coefficients of the beta-functions as well as absence of n-dependent phases for various n-point functions, as long as one assumes real coupling constants in the bulk Lagrangian.

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arXiv2012

Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence

We derive a collective field theory of the singlet sector of the Sp(2N) sigma model. Interestingly the hamiltonian for the bilocal collective field is the same as that of the O(N) model. However, the large-N saddle points of the two models differ by a sign. This leads to a fluctuation hamiltonian with a negative quadratic term and alternating signs in the nonlinear terms which correctly reproduces the correlation functions of the singlet sector. Assuming the validity of the connection between O(N) collective fields and higher spin fields in AdS, we argue that a natural interpretation of this theory is by a double analytic continuation, leading to the dS/CFT correspondence proposed by Anninos, Hartman and Strominger. The bi-local construction gives a map into the bulk of de Sitter space-time. Its geometric pseudospin-representation provides a framework for quantization and definition of the Hilbert space. We argue that this is consistent with finite N grassmanian constraints, establishing the bi-local representation as a nonperturbative framework for quantization of Higher Spin Gravity in de Sitter space.

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arXiv2012

Quantum Quench Across a Zero Temperature Holographic Superfluid Transition

We study quantum quench in a holographic model of a zero temperature insulator-superfluid transition. The model is a modification of that of arXiv:0911.0962 and involves a self-coupled complex scalar field, Einstein gravity with a negative cosmological constant, and Maxwell field with one of the spatial directions compact. In a suitable regime of parameters, the scalar field can be treated as a probe field whose backreaction to both the metric and the gauge field can be ignored. We show that when the chemical potential of the dual field theory lies between two critical values, the equilibrium background geometry is a AdS soliton with a constant gauge field, while the complex scalar condenses leading to broken symmetry. We then turn on a time dependent source for the order parameter which interpolates between constant values and crosses the order-disorder critical point. In the critical region adiabaticity breaks down, but for a small rate of change of the source $v$ there is a new small-$v$ expansion in fractional powers of $v$. The resulting critical dynamics is dominated by a zero mode of the bulk field. To lowest order in this small-$v$ expansion, the order parameter satisfies a time dependent Landau-Ginsburg equation which has $z=2$, but non-dissipative. These predictions are verified by explicit numerical solutions of the bulk equations of motion.

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arXiv2012

Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach

We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2+1 dimensions due to a time-dependent coupling in the large-$N$ limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large $N$ which determine the time dependent gap in terms of the coupling. These equations lead to a criterion for the breakdown of adiabaticity for slow variation of the coupling leading to a Kibble-Zurek scaling law. We describe a self-consistent numerical procedure to solve these large-$N$ equations and provide explicit numerical solutions for a coupling which starts deep in the gapped phase at early times and approaches the zero temperature equilibrium critical point $g_c$ in a linear fashion. We demonstrate that for such a protocol there is a value of the coupling $g= g_c^{\rm dyn}> g_c$ where the gap function vanishes, possibly indicating a dynamical instability. We study the dependence of $g_c^{\rm dyn}$ on both the rate of change of the coupling and the initial temperature. We also verify, by studying the evolution of the mass gap subsequent to a sudden change in $g$, that the model does not display thermalization within a finite time interval $t_0$ and discuss the implications of this observation for its conjectured gravitational dual as a higher spin theory in $AdS_4$.

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arXiv2011

Holographic Quantum Quench

We discuss recent results in the study of the evolution of strongly coupled field theories in the presence of time dependent couplings using the holographic correspondence. The aim is to understand (i) thermalization and (ii) universal behavior when the coupling crosses a critical point. Our emphasis is on situations where a subset of bulk fields can be treated in a probe approximation. We consider two different setups. In the first, defect conformal field theories are described by probe branes in AdS space-times, and an initial vacuum state evolves due to a time dependent coupling in the probe sector. While a black hole formation is invisible in this approximation, we show that thermalization can nevertheless happen - this is signalled by formation of apparent horizons on the brane worldvolume. In the second setup, we consider a probe bulk scalar field in the background of a AdS black brane. In equilibrium, this system undergoes a critical phase transition at some temperature when the source for the dual operator vanishes. For a time dependent source which goes across this critical point, we show that a zero mode of the bulk field dominates the dynamics and leads to scaling behavior of the order parameter as a function of the rate of change.

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