Showing papers by "Amit Dutta published in 2019"

Dynamical quantum phase transitions in extended toric-code models

Abstract: We study the nonequilibrium dynamics of the extended toric-code model (both ordered and disordered) to probe the existence of dynamical quantum phase transitions (DQPTs) We show that in the case of the ordered toric-code model, the zeros of Loschmidt overlap (generalized partition function) occur at critical times when DQPTs occur, which is confirmed by the nonanalyticities in the dynamical counterpart of the free-energy density Moreover, we show that DQPTs occur for any nonzero field strength if the initial state is the excited state of the toric-code model In the disordered case, we show that it is imperative to study the behavior of the first time derivative of the dynamical free-energy density averaged over all the possible configurations to characterize the occurrence of DQPTs in the disordered toric-code model since the disorder parameter itself acts as a new artificial dimension We also show that for the case where anyonic excitations are present in the initial state, the conditions for DQPTs to occur are the same as what happens in the absence of any excitation

Fibonacci steady states in a driven integrable quantum system

Abstract: We study an integrable system that is reducible to free fermions by a Jordan-Wigner transformation which is subjected to a Fibonacci driving protocol based on two noncommuting Hamiltonians. In the high-frequency limit $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty}$, we show that the system reaches a nonequilibrium steady state, up to some small fluctuations which can be quantified. For each momentum $k$, the trajectory of the stroboscopically observed state lies between two concentric circles on the Bloch sphere; the circles represent the boundaries of the small fluctuations. The residual energy is found to oscillate in a quasiperiodic way between two values which correspond to the two Hamiltonians that define the Fibonacci protocol. These results can be understood in terms of an effective Hamiltonian which simulates the dynamics of the system in the high-frequency limit.

Dynamical preparation of a topological state and out-of-equilibrium bulk-boundary correspondence in a Su-Schrieffer-Heeger chain under periodic driving

Abstract: Exploiting the possibility of temporal variation of the winding number, we have prepared a Su-Schrieffer-Heeger (SSH) chain in its stroboscopic topological state, starting from the trivial one, by application of a periodic perturbation. The periodic driving we employ here is adiabatically switched on to break the particle-hole symmetry and generate a chiral mass term in the effective Floquet Hamiltonian; consequently, the Floquet Hamiltonian also gets deformed without crossing the gapless quantum critical point. The particle-hole symmetry is subsequently restored in the Floquet Hamiltonian by adiabatically switching off a part of the periodic potential. Thereafter, the Floquet Hamiltonian develops a symmetry-protected nontrivial topological winding number. Furthermore, we also observe stroboscopic topologically protected localized edge states in a long open chain and show that a bulk-boundary correspondence survives a unitary nonequilibrium situation in one-dimensional BDI Hamiltonians. Moreover, considering an extended SSH chain with higher neighbor hoppings, we dynamically prepare the system in a stroboscopic out-of-equilibrium topological insulator state starting from a metallic regime. At the same time, we establish the dynamical preparation of higher winding phases in an extended SSH chain with stroboscopic bulk-boundary correspondence in the nonequilibrium state of the system.

One-dimensional quantum many body systems with long-range interactions.

Abstract: The presence of algebraically decaying long-range interactions may alter the critical as well as topological behaviour of a quantum many-body systems. However, when the interaction decays at a faster rate, the short-range behaviour is expected to be retrieved. Similarly, the long-range nature of interactions has a prominent signature on the out of equilibrium dynamics of these systems, e.g, in the growth of the entanglement entropy following a quench, the propagation of mutual information and non-equilibrium phase transitions. In this review, we summarize the results of long-range interacting classical and quantum Ising chains which have been studied since decades. Thereafter, we focus on the recent developments on the integrable long-range Kitaev chain emphasising the role of long-range superconducting pairing term on determining its topological phase diagram and out of equilibrium dynamics.

Critical phase boundaries of static and periodically kicked long-range Kitaev chain.

Abstract: We study the static and dynamical properties of a long-range Kitaev chain, i.e. a p -wave superconducting chain in which the superconducting pairing decays algebraically as [Formula: see text], where l is the distance between the two sites and [Formula: see text] is a positive constant. Considering very large system sizes, we show that when [Formula: see text], the system is topologically equivalent to the short-range Kitaev chain with massless Majorana modes at the ends of the system; on the contrary, for [Formula: see text], there exist symmetry protected massive Dirac end modes. We further study the dynamical phase boundary of the model when periodic [Formula: see text]-function kicks are applied to the chemical potential; we specially focus on the case [Formula: see text] and analyze the corresponding Floquet quasienergies. Interestingly, we find that new topologically protected massless end modes are generated at the quasienergy [Formula: see text] (where T is the time period of driving) in addition to the end modes at zero energies which exist in the static case. By varying the frequency of kicking, we can produce topological phase transitions between different dynamical phases. Finally, we propose some bulk topological invariants which correctly predict the number of massless end modes at quasienergies equal to 0 and [Formula: see text] for a periodically kicked system with [Formula: see text].

Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven Su-Schrieffer-Heeger chain

Abstract: Considering a BDI symmetric one-dimensional SSH model, we explore the fate of the bulk topological invariant, namely, the winding number under a generic time dependent perturbation; the effective Hamiltonian, that generates the temporal evolution of the initial (ground) state of the completely symmetric initial Hamiltonian, may have the same or different symmetries. To exemplify, we consider the following protocols, namely (i) a perfectly periodic protocol (ii) a periodic protocol with noisy perturbations and also (iii) sudden changes in the parameters of the initial Hamiltonian. We establish that the topological invariant may change in some cases when the effective Hamiltonian (or the Floquet Hamiltonian in the periodic situation when observed stroboscopically) does not respect all BDI symmetries; this is manifested in the associated particle (polarisation) or heat current in the bulk. Our results establish a strong connection between the time evolution of the winding number (thus, the associated transport of currents) and the symmetry of the Hamiltonian generating the time evolution which has been illustrated considering an exhaustive set of possibilities.

Quantum magnetometry using two-stroke thermal machines

Abstract: The precise estimation of small parameters is a challenging problem in quantum metrology. Here, we introduce a protocol for accurately measuring weak magnetic fields using a two-level magnetometer, which is coupled to two (hot and cold) thermal baths and operated as a two-stroke quantum thermal machine. Its working substance consists of a two-level system (TLS), generated by an unknown weak magnetic field acting on a qubit, and a second TLS arising due to the application of a known strong and tunable field on another qubit. Depending on this field, the machine may either act as an engine or a refrigerator. Under feasible conditions, determining this transition point allows to reduce the relative error of the measurement of the weak unknown magnetic field by the ratio of the temperatures of the colder bath to the hotter bath.