arXiv subjects

Krishnendu Sengupta

Publications and source records attributed to Krishnendu Sengupta.

10 recordsLinked to original sources

arXiv2026

Non-relativistic Floquet Conformal Field Theory

We develop a formalism for studying Floquet dynamics for systems with non-relativistic conformal invariance in d spatial dimensions. Our analysis indicates the existence of two dynamical phases, hyperbolic and elliptic, separated by a parabolic transition surface. We demonstrate this by studying the fidelity of the driven state and the expectation value of a conformal generator in the many body ground state during the drive. Stroboscopically, they behave exponentially in the hyperbolic phase, show oscillatory behavior in the elliptic phase, and exhibit power-law on the transition surface. Our analysis is completely universal and can be directly applied to several systems including trapped fermions near unitarity and resonant anyons. The former can provide experimental signatures of these dynamical phases. We also comment on a holographic perspective of such driven non-relativistic CFTs and demonstrate that the hyperbolic phase is associated with a timelike stationary-limit surface, such as an ergosphere, in the bulk, while the parabolic phase corresponds to an extremal Killing horizon.

hep-th↗

arXiv2025

Dynamical Phases of Higher Dimensional Floquet CFTs

This paper investigates the dynamical phases of Floquet Conformal Field Theories (CFTs) in space-time dimensions greater than two. Building upon our previous work [1] which introduced quaternionic representations for studying Floquet dynamics in higher dimensional CFTs, we now explore more general square pulse drive protocols that go beyond a single SU(1,1) subgroup. We demonstrate that, for multi-step drive protocols, the system exhibits distinct dynamical phases characterized by the nature of the eigenvalues of the quaternionic matrix representing time evolution in a single cycle, leading to different stroboscopic responses. Our analysis establishes a fundamental geometric interpretation where these dynamical phases directly correspond to the presence or absence of Killing horizons in the base space of the CFT and in a higher dimensional AdS space on which a putative dual lives. The heating phase is associated with a non-extremal horizon, the critical phase with an extremal horizon which disappears in the non-heating phase. We develop perturbative approaches to compute the Floquet Hamiltonians in different regimes and show, how tuning drive parameters can lead to horizons, providing a geometric framework for understanding heating phenomena in driven conformal systems.

hep-th↗

arXiv2023

Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two

We find classes of driven conformal field theories (CFT) in d + 1 dimensions with d > 1, whose quench and Floquet dynamics can be computed exactly. The setup is suitable for studying periodic drives, consisting of square pulse protocols for which Hamiltonian evolution takes place with different deformations of the original CFT Hamiltonian in successive time intervals. These deformations are realized by specific combinations of conformal generators with a deformation parameter $\beta$; the $\beta < 1$ ($\beta > 1$) Hamiltonians can be unitarily related to the standard (Luscher-Mack) CFT Hamiltonian. The resulting time evolution can be then calculated by conformal transformations. For $d\leq 3$ we show that the transformations can be obtained in a quaternion formalism. Evolution with such a single Hamiltonian yields qualitatively different time dependences of observables depending on the value of $\beta$, ranging from exponential decays characteristic of heating to oscillations and power law decays. This manifests in the behavior of the fidelity, unequal-time correlator, and the energy density at the end of a single cycle of a square pulse protocol with different hamiltonians in successive time intervals. When the Hamiltonians in a cycle involve generators of a single SU(1, 1) subalgebra we calculate the Floquet Hamiltonian. We show that one can get dynamical phase transitions by varying the time period of a cycle, where the system can go from a non-heating phase which is oscillatory as a function of the time period to a heating phase with an exponentially damped behavior. Our methods can be generalized to other discrete and continuous protocols. We also point out that our results are expected to hold for a broader class of QFTs that possesses an SL(2, C) symmetry with fields that transform as quasi-primaries under this. As an example, we briefly comment on celestial CFTs in this context.

hep-th↗

arXiv2021

Conformal Floquet dynamics with a continuous drive protocol

We study the properties {of a conformal field theory} (CFT) driven periodically with a continuous protocol characterized by a frequency $ω_D$. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator $U$. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for $U$ that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability ($P_n$), equal ($C_n$) and unequal ($G_n$) time two-point primary correlators, energy density($E_n$), and the $m^{\rm th}$ Renyi entropy ($S_n^m$) after $n$ drive cycles. Our results show that below a crossover stroboscopic time scale $n_c$, $P_n$, $E_n$ and $G_n$ exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of $C_n$, $G_n$ and $E_n$ for the continuous protocol and find emergence of spatial divergences of $C_n$ and $G_n$ in both the heating and non-heating phases. We express our results for $S_n^m$ and $C_n$ in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

hep-th↗

arXiv2020

Order parameter dynamics of the non-linear sigma model in the large $N$ limit

We study non-equilibrium order parameter dynamics of the non-linear sigma model in the large $N$ limit, using Keldysh formalism. We provide a scheme for obtaining stable numerical solutions of the Keldysh saddle point equations, and use them to study the order parameter dynamics of the model either following a ramp, or in the presence of a periodic drive. We find that the transient dynamics of the order parameter in the presence of a periodic drive is controlled by the drive frequency displaying the phenomenon of synchronization. We also study the approach of the order parameter to its steady state value following a ramp and find out the effective temperature of the steady state. We chart out the steady state temperature of the ordered phase as a function of ramp time and amplitude, and discuss the relation of our results to experimentally realizable spin models.

cond-mat.stat-mech↗

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.

hep-th↗

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.

hep-th↗

arXiv2011

Nonequilibrium dynamics of closed interacting quantum systems

This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. We discuss several aspects of the slow dynamics in driven systems and emphasize the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions. We also review recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis and discuss relaxation in integrable systems. Finally we overview key experiments probing quantum dynamics in cold atom systems and put them in the context of our current theoretical understanding.

cond-mat.stat-mech↗

arXiv2011

Non-equilibrium dynamics of Bosonic Mott insulators in an electric field

We study the non-equilibrium dynamics of one-dimensional Mott insulating bosons in the presence of a tunable effective electric field E which takes the system across a quantum critical point (QCP) separating a disordered and a translation symmetry broken ordered phase. We provide an exact numerical computation of the residual energy Q, the log-fidelity F, the excess defect density D, and the order parameter correlation function for a linear-in-time variation of E with a rate v. We discuss the temporal and spatial variation of these quantities for a range of v and for finite system sizes as relevant to realistic experimental setups [J. Simon et al., Nature 472, 307 (2011)]. We show that in finite-sized systems Q, F, and D obey Kibble-Zurek scaling, and suggest further experiments within this setup to test our theory.

cond-mat.quant-gas↗

arXiv2009

Commensurate lock-in and incommensurate supersolid phases of hardcore bosons on anisotropic triangular lattices

We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hardcore bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wavevectors are locked to commensurate values and jump between adjacent supersolids. In the thermodynamic limit, however, the magnitude of these jumps vanishes leading to a continuous set of novel incommensurate supersoild phases.

cond-mat.str-el↗