arXiv subjects

Roopayan Ghosh

Publications and source records attributed to Roopayan Ghosh.

25 records · Page 2Linked to original sources

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↗

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

Disorder-induced Enhancement of Entanglement Growth in One Dimension: Information Leakage at the scale of localization length

When a group of compactly packed free fermions is allowed to spread over an empty one-dimensional lattice, the spreading particles can create entanglement between different parts of the lattice. We show, though breaking of translational invariance (TI) of the lattice by disorder slows down the spreading of local observables, the entanglement entropy of a subsystem can nonetheless receive a remarkable enhancement as long as the subsystem lies within the single-particle localization length. We show, the main mechanism behind this enhancement is the re-entrant exchange of particles between the subparts due to transport of mutual information due to back scattering. We discuss the length and time scales relevant to the phenomenon. We study the phenomenon for breaking of TI by both quasi-periodic and random potentials. We further explore the effect of randomness only in the initial state. This also exhibits a similar enhancement effect even in a TI lattice. We also touch upon the special case of periodic potential, where qualitatively similar phenomenology emerges, though the coherence in the back scattering in this case leads to effects not captured by our simple yet generic picture.

cond-mat.str-el↗

arXiv2020

A Floquet perturbation theory for periodically driven weakly-interacting fermions

We compute the Floquet Hamiltonian $H_F$ for weakly interacting fermions subjected to a continuous periodic drive using a Floquet perturbation theory (FPT) with the interaction amplitude being the perturbation parameter. This allows us to address the dynamics of the system at intermediate drive frequencies $\hbar ω_D \ge V_0 \ll {\mathcal J}_0$, where ${\mathcal J}_0$ is the amplitude of the kinetic term, $ω_D$ is the drive frequency, and $V_0$ is the typical interaction strength between the fermions. We compute, for random initial states, the fidelity $F$ between wavefunctions after a drive cycle obtained using $H_F$ and that obtained using exact diagonalization (ED). We find that FPT yields a substantially larger value of $F$ compared to its Magnus counterpart for $V_0\le \hbar ω_D$ and $V_0\ll {\mathcal J}_0$. We use the $H_F$ obtained to study the nature of the steady state of an weakly interacting fermion chain; we find a wide range of $ω_D$ which leads to subthermal or superthermal steady states for finite chains. The driven fermionic chain displays perfect dynamical localization for $V_0=0$; we address the fate of this dynamical localization in the steady state of a finite interacting chain and show that there is a crossover between localized and delocalized steady states. We discuss the implication of our results for thermodynamically large chains and chart out experiments which can test our theory.

cond-mat.str-el↗

arXiv2020

Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach

We present a path integral formalism for expressing matrix elements of the density matrix of a quantum many-body system between any two coherent states in terms of standard Matsubara action with periodic(anti-periodic) boundary conditions on bosonic(fermionic) fields. We show that this enables us to express several entanglement measures for bosonic/fermionic many-body systems described by a Gaussian action in terms of the Matsubara Green function. We apply this formalism to compute various entanglement measures for the two-dimensional Bose-Hubbard model in the strong-coupling regime, both in the presence and absence of Abelian and non-Abelian synthetic gauge fields, within a strong coupling mean-field theory. In addition, our method provides an alternative formalism for addressing time evolution of quantum-many body systems, with Gaussian actions, driven out of equilibrium without the use of Keldysh technique. We demonstrate this by deriving analytical expressions of the return probability and the counting statistics of several operators for a class of integrable models represented by free Dirac fermions subjected to a periodic drive in terms of the elements of their Floquet Hamiltonians. We provide a detailed comparison of our method with the earlier, related, techniques used for similar computations, discuss the significance of our results, and chart out other systems where our formalism can be used.

cond-mat.str-el↗

arXiv2018

Magnetization induced dynamics of a Josephson junction coupled to a nanomagnet

We study the superconducting current of a Josephson junction (JJ) coupled to an external nanomagnet driven by a time dependent magnetic field both without and in the presence of an external AC drive. We provide an analytic, albeit perturbative, solution for the Landau-Lifshitz (LL) equations governing the coupled JJ-nanomagnet system in the presence of a magnetic field with arbitrary time-dependence oriented along the easy axis of the nanomagnet's magnetization and in the limit of weak dimensionless coupling $ε_0$ between the JJ and the nanomagnet. We show the existence of Shapiro-like steps in the I-V characteristics of the JJ subjected to a voltage bias for a constant or periodically varying magnetic field and explore the effect of rotation of the magnetic field and the presence of an external AC drive on these steps. We support our analytic results with exact numerical solution of the LL equations. We also extend our results to dissipative nanomagnets by providing a perturbative solution to the Landau-Lifshitz-Gilbert (LLG) equations for weak dissipation. We study the fate of magnetization-induced Shapiro steps in the presence of dissipation both from our analytical results and via numerical solution of the coupled LLG equations. We discuss experiments which can test our theory.

cond-mat.supr-con↗

arXiv2018

Ramp and periodic dynamics across non-Ising critical points

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a $Z_3$ or $Z_4$ symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with $L \le 24$ using exact-diagonalization (ED), of the excitation density $D$, the wavefunction overlap $F$, and the excess energy $Q$ at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which $D$ and $Q$ shows Kibble-Zurek scaling. We find, based on numerical analysis with $L \le 24$, that such scaling is consistent with that expected from critical exponents of the $q$-state Potts universality class with $q=3,4$. For periodic protocol, we show that the model display near-perfect dynamical freezing at specific frequencies; at these frequencies $D, Q \to 0$ and $|F| \to 1$. We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

cond-mat.str-el↗