arXiv subjects

K. Sengupta

Publications and source records attributed to K. Sengupta.

At least 37 records · Page 2Linked to original sources

arXiv2024

Signatures of fragmentation for periodically driven fermions

We study the possible signatures of prethermal strong Hilbert space fragmentation (HSF) for one-dimensional (1D) fermions subjected to a periodic drive. We extend the results of Phys. Rev. Lett. 130, 120401 (2023) to show the possibility of such fragmentation for a large class of experimentally relevant drive protocols. Moreover, we demonstrate the persistence of HSF when the fermion chain is taken away from half-filling. Both these analysis indicate the robustness of the fragmentation phenomenon reported earlier. We also provide an alternate derivation of the Floquet Hamiltonian of the driven chain which yields insight into the generic nested commutator structure of its higher order terms. Finally, we study the density-density out-of-time-correlators (OTOC) of the driven chain both away and near the special drive frequencies at which its first order Floquet Hamiltonian exhibits fragmentation. We show that these OTOCs, for a chain with open boundary condition, exhibit a distinct periodic unscrambling of information at special drive frequencies; such unscrambling can therefore serve as a marker of prethermal HSF. We provide an approximate analytic explanation of the role of HSF behind such periodic unscrambling and discuss experiments which can detect signatures of strong HSF in such driven chains.

cond-mat.str-el↗

arXiv2023

Non-equilibrium dynamics of bosons with dipole symmetry: Large-$N$ Keldysh approach

We study the quench and the ramp dynamics of interacting $N$-component charged bosons with dipole symmetry using Schwinger-Keldysh field theory in the large $N$ limit. The equilibrium phase diagram of these bosons shows two phases in the large $N$ limit. The first is a normal phase where both the global $U(N)$ and the dipole symmetries are conserved and the second is a delocalized condensed phase where both the symmetries are broken. In contrast, our explicit computation of the steady state after an instantaneous quantum quench from the condensed phase shows that an additional, novel, delocalized normal phase, where the global $U(N)$ symmetry is conserved but the dipole symmetry is broken, can exist for a range of quench parameters. A study of ramp dynamics of the model shows that the above-mentioned steady state exists only above a critical ramp rate which we estimate.

cond-mat.quant-gas↗

arXiv2023

Entanglement transitions in a periodically driven non-Hermitian Ising chain

We study entanglement transitions in a periodically driven Ising chain in the presence of an imaginary transverse field $γ$ as a function of drive frequency $ω_D$. In the high drive amplitude and frequency regime, we find a critical value $γ=γ_c$ below which the steady state half-chain entanglement entropy, $S_{L/2}$, scales with chain length $L$ as $S_{L/2} \sim \ln L$; in contrast, for $γ>γ_c$, it becomes independent of $L$. In the small $γ$ limit, we compute the coefficient, $α$, of the $\ln L$ term analytically using a Floquet perturbation theory and trace its origin to the presence of Fisher-Hartwig jump singularities in the correlation function of the driven chain. We also study the frequency dependence of $γ_c$ and show that $γ_c \to 0$ at special drive frequencies; at these frequencies, which we analytically compute, $S_{L/2}$ remain independent of $L$ for all $γ$. This behavior can be traced to an approximate emergent symmetry of the Floquet Hamiltonian at these drive frequencies which we identify. Finally, we discus the behavior of the driven system at low and intermediate drive frequencies. Our analysis shows the presence of volume law behavior of the entanglement in this regime $S_{\ell} \sim \ell$ for small subsystem length $\ell \le \ell^{\ast}(ω_D)$. We identify $\ell^{\ast}(ω_D)$ and tie its existence to the effective long-range nature of the Floquet Hamiltonian of the driven chain for small subsystem size. We discuss the applicability of our results to other integrable non-hermitian models.

cond-mat.str-el↗

arXiv2023

Detecting prethermal Floquet phases of Rydberg atom arrays

We study the prethermal Floquet phases of a two-dimensional (2D) Rydberg atom array on a rectangular lattice in the presence of a periodic drive with large drive amplitude. We derive an analytic, albeit perturbative, Floquet Hamiltonian using Floquet perturbation theory (FPT) which charts out these phases and shows that the transition between them can be accessed by tuning the drive frequency. Using both numerical exact diagonalization on finite-size arrays and analytical first-order Floquet Hamiltonian derived using FPT, we show that these prethermal Floquet phases and the transitions between them can be detected by studying the dynamics of equal-time density-density correlation functions of the Rydberg atoms. Our analysis thus provides a simple way of detecting these phases and associated transitions in this system; such a detection can be achieved in standard experiments which we discuss.

cond-mat.str-el↗

arXiv2023

Strong Hilbert space fragmentation via emergent quantum drums in two dimensions

We introduce a disorder-free model of $S=1/2$ spins on the square lattice in a constrained Hilbert space where two up-spins are not allowed simultaneously on any two neighboring sites of the lattice. The interactions are given by ring-exchange terms on elementary plaquettes that conserve both the total magnetization as well as dipole moment. We show that this model provides a tractable example of strong Hilbert space fragmentation in two dimensions with typical initial states evading thermalization with respect to the full Hilbert space. Given any product state, the system can be decomposed into disjoint spatial regions made of edge and/or vertex sharing plaquettes that we dub as ``quantum drums''. These quantum drums come in many shapes and sizes and specifying the plaquettes that belong to a drum fixes its spectrum. The spectra of some small drums is calculated analytically. We study two bigger quasi-one-dimensional drums numerically, dubbed ``wire'' and a ``junction of two wires'' respectively. We find that these possess a chaotic spectrum but also support distinct families of quantum many-body scars that cause periodic revivals from different initial states. The wire is shown to be equivalent to the one-dimensional PXP chain with open boundaries, a paradigmatic model for quantum many-body scarring; while the junction of two wires represents a distinct constrained model.

cond-mat.stat-mech↗

arXiv2023

Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states

We study if periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases which have no counterparts in the static model. Specifically, we consider the Aubry-André model which is a one-dimensional time-independent model with an on-site quasiperiodic potential $V_0$ and a nearest-neighbor hopping amplitude which is taken to have a staggered form. We add a uniform hopping amplitude which varies periodically in time with a frequency $ω$. Unlike the static Aubry-André model which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases: a phase with only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios which scale with the system size with exponents which are different from the values for both extended and localized states. In addition, we observe intricate re-entrant transitions between the different kinds of states when $ω$ and $V_0$ are varied. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet and find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a non-monotonic dependence on $V_0$ which does not occur in the static model. We conclude that the interplay of quasiperiodic potential and driving produces a rich phase diagram which does not appear in the static model.

cond-mat.dis-nn↗

arXiv2022

Prethermal fragmentation in a periodically driven Fermionic chain

We study a Fermionic chain with nearest-neighbor hopping and density-density interactions, where the nearest-neighbor interaction term is driven periodically. We show that such a driven chain exhibits prethermal strong Hilbert space fragmentation (HSF) in the high drive amplitude regime at specific drive frequencies $ω_m^{\ast}$. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of $ω_m^{\ast}$ using a Floquet perturbation theory and provide exact numerical computation of entanglement entropy, equal-time correlation functions, and the density autocorrelation of Fermions for finite chains. All of these quantities indicate clear signatures of strong HSF. We study the fate of the HSF as one tunes away from $ω_m^{\ast}$ and discuss the extent of the prethermal regime as a function of the drive amplitude.

cond-mat.str-el↗

arXiv2022

Brane Detectors of a Dynamical Phase Transition in a Driven CFT

We show that a dynamical transition from a non-heating to a heating phase of a periodic $SL(2,\mathbb{R})$ driven two-dimensional conformal field theory (CFT) with a large central charge is perceived as a first order transition by a bulk brane embedded in the dual AdS. We construct the dual bulk metric corresponding to a driven CFT for both the heating and the non-heating phases. These metrics are different AdS$_{2}$ slices of the pure AdS$_{3}$ metric. We embed a brane in the obtained dual AdS space and provide an explicit computation of its free energy both in the probe limit and for an end-of-world (EOW) brane taking into account its backreaction. Our analysis indicates a finite discontinuity in the first derivative of the brane free energy as one moves from the non-heating to the heating phase (by tuning the drive amplitude and/or frequency of the driven CFT) thus demonstrating the presence of the bulk first order transition. Interestingly, no such transition is perceived by the bulk in the absence of the brane. We also provide explicit computations of two-point, four-point out-of-time correlators (OTOC) using the bulk picture. Our analysis shows that the structure of these correlators in different phases match their counterparts computed in the driven CFT. We analyze the effect of multiple EOW branes in the bulk and discuss possible extensions of our work for richer geometries and branes.

hep-th↗

arXiv2022

Emergent conservation in Floquet dynamics of integrable non-Hermitian models

We study the dynamics of a class of integrable non-Hermitian free-fermionic models driven periodically using a continuous drive protocol characterized by an amplitude $g_1$ and frequency $ω_D$. We derive an analytic, albeit perturbative, Floquet Hamiltonian for describing such systems using Floquet perturbation theory with $g_1^{-1}$ being the perturbation parameter. Our analysis indicates the existence of special drive frequencies at which an approximately conserved quantity emerges. The presence of such an almost conserved quantity is reflected in the dynamics of the fidelity, the correlation functions and the half-chain entanglement entropy of the driven system. In addition, it also controls the nature of the steady state of the system. We show that one-dimensional (1D) transverse field Ising model, with an imaginary component of the transverse field, serves as an experimentally relevant example of this phenomenon. In this case, the transverse magnetization is approximately conserved; this conservation leads to complete suppression of oscillatory features in the transient dynamics of fidelity, magnetization, and entanglement of the driven chain at special drive frequencies. We discuss the nature of the steady state of the Ising chain near and away from these special frequencies, demonstrate the protocol independence of this phenomenon by showing its existence for discrete drive protocols, and suggest experiments which can test our theory.

cond-mat.stat-mech↗

arXiv2022

Quantum order-by-disorder induced phase transition in Rydberg ladders with staggered detuning

$^{87}{\rm Rb}$ atoms are known to have long-lived Rydberg excited states with controllable excitation amplitude (detuning) and strong repulsive van der Waals interaction $V_{{\bf r} {\bf r'}}$ between excited atoms at sites ${\bf r}$ and ${\bf r'}$. Here we study such atoms in a two-leg ladder geometry in the presence of both staggered and uniform detuning with amplitudes $Δ$ and $λ$ respectively. We show that when $V_{\bf r r'} \gg(\ll) Δ, λ$ for $|{\bf r}-{\bf r'}|=1(>1)$, these ladders host a plateau for a wide range of $λ/Δ$ where the ground states are selected by a quantum order-by-disorder mechanism from a macroscopically degenerate manifold of Fock states with fixed Rydberg excitation density $1/4$. Our study further unravels the presence of an emergent Ising transition stabilized via the order-by-disorder mechanism inside the plateau. We identify the competing terms responsible for the transition and estimate a critical detuning $λ_c/Δ=1/3$ which agrees well with exact-diagonalization based numerical studies. We also study the fate of this transition for a realistic interaction potential $V_{{\bf r} {\bf r'}} = V_0 /|{\bf r}-{\bf r'}|^6$, demonstrate that it survives for a wide range of $V_0$, and provide analytic estimate of $λ_c$ as a function of $V_0$. This allows for the possibility of a direct verification of this transition in standard experiments which we discuss.

cond-mat.str-el↗

arXiv2022

Hinge mode dynamics of periodically driven higher-order Weyl semimetals

We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime for both discrete (square pulse) and continuous (cosine) periodic drive protocols. We analyze the Floquet phases of this system and show that its quasienergy spectrum becomes almost gapless in the large drive amplitude regime at special drive frequencies. Away from these frequencies, the gapped quasienergy spectrum supports weakly dispersing Floquet hinge modes. Near them, these hinge modes penetrate into the bulk and eventually become indistinguishable from the bulk modes. We provide an analytic, albeit perturbative, expression for the Floquet Hamiltonian using Floquet perturbation theory (FPT) which explains this phenomenon and leads to analytic expressions of these special frequencies. We also show that in the large drive amplitude regime, the zero energy hinge modes corresponding to the static tight-binding Hamiltonian display qualitatively different dynamics at these special frequencies. We discuss possible local density of state measurement using a scanning tunneling microscope which can test our theory.

cond-mat.mes-hall↗

arXiv2022

Out-of-Time-Order correlators in driven conformal field theories

We compute Out-of-Time-Order correlators (OTOCs) for conformal field theories (CFTs) subjected to either continuous or discrete periodic drive protocols. This is achieved by an appropriate analytic continuation of the stroboscopic time. After detailing the general structure, we perform explicit calculations in large-$c$ CFTs where we find that OTOCs display an exponential, an oscillatory and a power-law behaviour in the heating phase, the non-heating phase and on the phase boundary, respectively. In contrast to this, for the Ising CFT representing an integrable model, OTOCs never display such exponential growth. This observation hints towards how OTOCs can demarcate between integrable and chaotic CFT models subjected to a periodic drive. We further explore properties of the light-cone which is characterized by the corresponding butterfly velocity as well as the Lyapunov exponent. Interestingly, as a consequence of the spatial inhomogeneity introduced by the drive, the butterfly velocity, in these systems, has an explicit dependence on the initial location of the operators. We chart out the dependence of the Lyapunov exponent and the butterfly velocities on the frequency and amplitude of the drive for both protocols and discuss the fixed point structure which differentiates such driven CFTs from their un-driven counterparts.

hep-th↗

arXiv2021

Periodically driven Rydberg chains with staggered detuning

We study the stroboscopic dynamics of a periodically driven finite Rydberg chain with staggered ($Δ$) and time-dependent uniform ($λ(t)$) detuning terms using exact diagonalization (ED). We show that at intermediate drive frequencies ($ω_D$), the presence of a finite $Δ$ results in violation of the eigenstate thermalization hypothesis (ETH) via clustering of Floquet eigenstates. Such clustering is lost at special commensurate drive frequencies for which $\hbar ω_d=n Δ$ ($n \in Z$) leading to restoration of ergodicity. The violation of ETH in these driven finite-sized chains is also evident from the dynamical freezing displayed by the density-density correlation function at specific $ω_D$. Such a correlator exhibits stable oscillations with perfect revivals when driven close to the freezing frequencies for initial all spin-down ($|0\rangle$) or Neel ($|{\mathbb Z}_2\rangle$, with up-spins on even sites) states. The amplitudes of these oscillations vanish at the freezing frequencies and reduces upon increasing $Δ$; their frequencies, however, remains pinned to $Δ/\hbar$ in the large $Δ$ limit. In contrast, for the $|{\bar {\mathbb Z}_2}\rangle$ (time-reversed partner of $|{\mathbb Z}_2\rangle$) initial state, we find complete absence of such oscillations leading to freezing for a range of $ω_D$; this range increases with $Δ$. We also study the properties of quantum many-body scars in the Floquet spectrum of the model as a function of $Δ$ and show the existence of novel mid-spectrum scars at large $Δ$. We supplement our numerical results with those from an analytic Floquet Hamiltonian computed using Floquet perturbation theory (FPT) and also provide a semi-analytic computation of the quantum scar states within a forward scattering approximation (FSA).

cond-mat.str-el↗

arXiv2021

Dynamical relaxation of correlators in periodically driven integrable quantum systems

We show that the correlation functions of a class of periodically driven integrable closed quantum systems approach their steady state value as $n^{-(α+1)/β}$, where $n$ is the number of drive cycles and $α$ and $β$ denote positive integers. We find that generically $β=2$ within a dynamical phase characterized by a fixed $α$; however, its value can change to $β=3$ or $β=4$ either at critical drive frequencies separating two dynamical phases or at special points within a phase. We show that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and one-dimensional (1D) transverse field Ising models, discuss the role of symmetries of the Floquet spectrum in determining $β$, and chart out the values of $α$ and $β$ realized in these models. We analyze the SSH model for a continuous drive protocol using a Floquet perturbation theory which provides analytical insight into the behavior of the correlation functions in terms of its Floquet Hamiltonian. This is supplemented by an exact numerical study of a similar behavior for the 1D Ising model driven by a square pulse protocol. For both models, we find a crossover timescale $n_c$ which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency, $ω_c$, is approached from below ($ω< ω_c$). We tie such behavior to the presence of multiple stationary points in the Floquet spectrum of these models and provide an analytic expression for the time period of these oscillations.

cond-mat.stat-mech↗

arXiv2021

Minimal model for Hilbert space fragmentation with local constraints

Motivated by previous works on a Floquet version of the PXP model [Mukherjee {\it et al.} Phys. Rev. B 102, 075123 (2020), Mukherjee {\it et al.} Phys. Rev. B 101, 245107 (2020)], we study a one-dimensional spin-$1/2$ lattice model with three-spin interactions in the same constrained Hilbert space (where all configurations with two adjacent $S^z=\uparrow$ spins are excluded). We show that this model possesses an extensive fragmentation of the Hilbert space which leads to a breakdown of thermalization upon unitary evolution starting from a large class of simple initial states. Despite the non-integrable nature of the Hamiltonian, many of its high-energy eigenstates admit a quasiparticle description. A class of these, which we dub as "bubble eigenstates", have integer eigenvalues (including mid-spectrum zero modes) and strictly localized quasiparticles while another class contains mobile quasiparticles leading to a dispersion in momentum space. Other anomalous eigenstates that arise due to a {\it secondary} fragmentation mechanism, including those that lead to flat bands in momentum space due to destructive quantum interference, are also discussed. The consequences of adding a (non-commuting) staggered magnetic field and a PXP term respectively to this model, where the former preserves the Hilbert space fragmentation while the latter destroys it, are discussed. A Floquet version with time-dependent staggered field also evades thermalization with additional features like freezing of exponentially many states at special drive frequencies. Finally, we map the model to a $U(1)$ lattice gauge theory coupled to dynamical fermions and discuss the interpretation of some of these anomalous states in this language. A class of gauge-invariant states show reduced mobility of the elementary charged excitations with only certain charge-neutral objects being mobile suggesting a connection to fractons.

cond-mat.str-el↗

arXiv2021

Phases and dynamics of ultracold bosons in a tilted optical lattice

We present a brief overview of the phases and dynamics of ultracold bosons in an optical lattice in the presence of a tilt. We begin with a brief summary of the possible experimental setup for generating the tilt. This is followed by a discussion of the effective low-energy model for these systems and its equilibrium phases. We also chart the relation of this model to the recently studied system of ultracold Rydberg atoms. Next, we discuss the non-equilibrium dynamics of this model for quench, ramp and periodic protocols with emphasis on the periodic drive which can be understood in terms of an analytic, albeit perturbative, Floquet Hamiltonian derived using Floquet perturbation theory (FPT). Finally, taking cue from the Floquet Hamiltonian of the periodically driven tilted boson chain, we discuss a spin model which exhibits Hilbert space fragmentation and exact dynamical freezing for wide range of initial states.

cond-mat.quant-gas↗

arXiv2021

Signatures of multifractality in a periodically driven interacting Aubry-André model

We study the many-body localization (MBL) transition of Floquet eigenstates in a driven, interacting fermionic chain with an incommensurate Aubry-André potential and a time-periodic hopping amplitude as a function of the drive frequency $ω_D$ using exact diagonalization (ED). We find that the nature of the Floquet eigenstates change from ergodic to Floquet-MBL with increasing frequency; moreover, for a significant range of intermediate $ω_D$, the Floquet eigenstates exhibit non-trivial fractal dimensions. We find a possible transition from the ergodic to this multifractal phase followed by a gradual crossover to the MBL phase as the drive frequency is increased. We also study the fermion auto-correlation function, entanglement entropy, normalized participation ratio (NPR), fermion transport and the inverse participation ratio (IPR) as a function of $ω_D$. We show that the auto-correlation, fermion transport and NPR displays qualitatively different characteristics (compared to their behavior in the ergodic and MBL regions) for the range of $ω_D$ which supports multifractal eigenstates. In contrast, the entanglement growth in this frequency range tend to have similar features as in the MBL regime; its rate of growth is controlled by $ω_D$. Our analysis thus indicates that the multifractal nature of Floquet-MBL eigenstates can be detected by studying auto-correlation function and fermionic transport of these driven chains. We support our numerical results with a semi-analytic expression of the Floquet Hamiltonian obtained using Floquet perturbation theory (FPT) and discuss possible experiments which can test our predictions.

cond-mat.dis-nn↗

arXiv2021

Mobility edge and multifractality in a periodically driven Aubry-André model

We study the localization-delocalization transition of Floquet eigenstates in a driven fermionic chain with an incommensurate Aubry-André potential and a hopping amplitude which is varied periodically in time. Our analysis shows the presence of a mobility edge separating single-particle delocalized states from localized and multifractal states in the Floquet spectrum. Such a mobility edge does not have any counterpart in the static Aubry-André model and exists for a range of drive frequencies near the critical frequency at which the transition occurs. The presence of the mobility edge is shown to leave a distinct imprint on fermion transport in the driven chain; it also influences the Shannon entropy and the survival probability of the fermions at long times. In addition, we find the presence of CAT states in the Floquet spectrum with weights centered around a few nearby sites of the chain. This is shown to be tied to the flattening of Floquet bands over a range of quasienergies. We support our numerical studies with a semi-analytic expression for the Floquet Hamiltonian ($H_F$) computed within a Floquet perturbation theory. The eigenspectra of the perturbative $H_F$ so obtained exhibit qualitatively identical properties to the exact eigenstates of $H_F$ obtained numerically. Our results thus constitute an analytic expression of a $H_F$ whose spectrum supports multifractal and CAT states. We suggest experiments which can test our theory.

cond-mat.stat-mech↗