Research work

Percolation transition in a topological phase

We study the signatures of the percolation transition in the topological phases of the short-ranged and long-ranged Su-Schrieffer-Heeger (SSH) chains. Under bond-percolation in both the chains, when the end-to-end connectivity is lost, the topological response (polarization) immediately becomes zero. However, the bond-diluted chain can host an extensive number of zero-modes even in the absence of the topological responses, indicating the breakdown of the bulk-edge correspondence. We label this region as a “fractured topological region” (FTR). We find that the presence of topological response of the chain is governed by the geometrical connectivity while the existence of zero-modes is determined by the critical lines of an effective ‘mean-field’ model. Thus, the interplay of topology and percolation gives rise to two different crossover boundaries in the phase diagram of the bond-diluted chain.  This work has been published as : Saikat Mondal, Subrata Pachhal, Adhip Agarwala, “Percolation transition in a topological phase”, Phys. Rev. B 108, L220201 (2023).

Fig. :  Polarization (P) as a function of α and p for long-range bond-percolated SSH chain with |w|/|v| = 5.0 and L = 64. Here, p_c is classical percolation threshold, p* denotes geometrical end-to-end connectivity and p_MF is the mean-field critical point. Configuration averaging is performed over 200 realizations. [Ref. : Phys. Rev. B 108, L220201 (2023)]

Signatures of quantum criticality in a dissipative system

We study the steady-state and early-time behaviour of a Kitaev chain coupled to both fermion-pumping (source) and fermion-decaying (sink) bath. We find that the steady-state of the chain can behave as a thermal state for some parameter regimes where the dissipative Kitaev chain can be mapped to classical spins in a magnetic field and an effective temperature. Interestingly, magnetization in the steady state can capture the signatures of quantum criticality of the Kitaev chain. Similarly, the early-time survival probability can also contain some signatures of quantum phase transitions. Thus, we show that the dissipative free-fermionic systems can contain the signatures of quantum criticality in both the early-time dynamics and the steady state.  Our work connects the fields of quantum criticality with classical paramagnetism and thermalization. This work has been published as : Rohan Joshi, Saikat Mondal, Souvik Bandyopadhyay, Sourav Bhattacharjee, Adhip Agarwala, “Signatures of quantum phases in a dissipative system”, Journal of Physics: Condensed Matter 36 (2024) 275601. 

Fig. : d(1/τD)/dμ (where survival probability F(t) ∼ exp(−t/τD)) as a function of μ and Δ for fermion-decaying bath (α=0.01, β =0). Here, μ=1 and μ = −1 are the critical lines. [Ref. : Journal of Physics: Condensed Matter 36 (2024) 275601]

Disconnected entanglement entropy (DEE) as a marker of edge-modes in a periodically driven Kitaev chain

We study the disconnected entanglement entropy (DEE) of a Kitaev chain in which the chemical potential is periodically modulated with δ-function pulses within the framework of Floquet theory. For this driving protocol, the DEE of a sufficiently large system with open boundary conditions turns out to be integer-quantized, with the integer being equal to the number of Majorana edge modes localized at each edge of the chain generated by the periodic driving, thereby establishing the DEE as a marker for detecting Floquet Majorana edge modes. Analyzing the DEE, we further show that these Majorana edge modes are robust against weak spatial disorder and temporal noise. Interestingly, we find that the DEE may, in some cases, also detect the anomalous edge modes which can be generated by periodic driving of the nearest-neighbor hopping, even though such modes have no topological significance and not robust against spatial disorder. We also probe the behavior of the DEE for a kicked Ising chain in the presence of an integrability breaking interaction which has been experimentally realized. This work has been published as Journal of Physics: Condensed Matter 35 (2023) 085601.

Fig. :  DEE (SD) in units of ln(2) as a function of the length L (in semi-log scale) of a Kitaev chain at ω = 1.0.  [Ref. : Journal of Physics: Condensed Matter 35 (2023) 085601.]

Periodically driven many-body quantum battery

A many-body quantum battery is a collection of many quantum systems (e.g., spin-1/2 systems), which can be considered as a quantum analogue to a classical battery. In the charging process of a quantum battery, energy is stored in a quantum battery through the application of a charging Hamiltonian. In this work, we have explored the charging of a spin-chain quantum battery through the periodic modulation of a transverse-field Ising Hamiltonian (TFIH). For this driving protocol, we have found that due to the resonance tunneling, the maxima of the stored energy and the minima of the variance of the battery Hamiltonian occur at some specific drive frequencies. Thus, with the suitable tuning of the drive frequency, the stored energy can be maximized and better stability of the stored energy can be provided (as the minimum value of the variance of the battery Hamiltonian corresponds to better stability of the stored energy). When the integrability is broken in the presence of an additional, time-periodic, longitudinal field in the TFIH, then we have found that the effective Floquet Hamiltonian contains terms which couple multiple spins and this may lead to a global charging of the battery at sufficiently low drive-frequency. However, for this protocol, we have found that the average charging power P (i.e., energy stored per unit time) scales linearly with the number of spins (N) in the chain, i.e., P ∼ N. On the contrary, a super-linear scaling of the charging power (P ∼ N^ x , with x > 1, where N is the number of spins in the chain) is a requirement for the quantum advantage and faster charging of the battery. As we have found that the average charging power does not scale super-linearly with the number of spins in the chain, there is no quantum advantage in the charging power for this driving protocol. This demonstrates that global charging is only a necessary and not a sufficient condition for achieving the quantum advantage. This work has been published as Phys. Rev. E 105, 044125 (2022).    

Fig. : Stored energy ( E ) and the variance of the battery Hamiltonian (ΔH_B)^2 as the functions of drive frequency (ω) for the charging of a spin-chain quantum battery composed of N = 200 spins through the transverse field Ising Hamiltonian (TFIH) with the transverse field h_z = 2.0. We observe that the maxima of the stored energy ( E ) coincide with the minima of (ΔH_B)^2.  [Ref. : Phys. Rev. E 105, 044125 (2022)]

Detection of topological phase transitions in a long-range Kitaev chain through the disconnected entanglement entropy (DEE)

 The disconnected entanglement entropy (DEE) is a measure of entanglement in a one dimensional system with disconnected partitions. It counts the number of the edge-modes by extracting the entanglement between them in a one-dimensional, short-ranged topological system. In this work, we have explored the applicability of the DEE in the detection of topological phase transition in a long-range Kitaev chain with the open boundary conditions where the strength of the superconducting pairing decays as a power law with the distance (r) between the fermions (∼ 1 / r^ α ) with an exponent α > 0. It is noteworthy that the topological phase transition is characterized by the vanishing of the bulk energy-gap at a quantum critical point (QCP). We have shown that while the DEE may not remain invariant deep within the topologically nontrivial phase when α < 1, it nevertheless shows a quantized discontinuous jump at the quantum critical point and can act as a strong marker for the detection of topological phase transition. We have also studied the time evolution of the DEE after a sudden quench of the chemical potential within the same phase. In the short-range limit of a finite-size chain, the DEE is expected to remain constant up to a critical time after the quench, which diverges in the thermodynamic limit. However, the critical time turns out to be zero when the long-range couplings dominate (i.e., α < 1). This work has been published as Phys. Rev. B 105, 085106 (2022)   

Fig. : DEE ( S_D ) in the units of ln(2) as a function of the chemical potential (μ) for a long-range Kitaev chain having L = 100 fermions in the open boundary conditions with different values of α < 1. The DEE shows discontinuous jump only at the QCP located at μ = 1 for α < 1. [Ref : Phys. Rev. B 105, 085106 (2022)] 

Dynamics of open quantum systems and applications to quantum thermal machines and quantum thermometry

Open quantum systems are the microscopic systems which interact with the environment(bath). Because of the interaction between the system and the bath, time evolution of the reduced density matrix of the system can not be represented by unitary dynamics. We have explored the dynamics of reduced density matrix of the sub-system weakly coupled to a hot bath and a cold bath  in presence of periodically driven system Hamiltonian in Lindblad framework. Then the concepts of Lindblad framework have been applied to quantum thermal machines and quantum thermometry.

If a two-level system (TLS) is weakly coupled to a hot bath and a cold bath and the system Hamiltonian is periodically modulated with an asymmetric rectangular pulse, then we have found that, it is possible to make a transition from heat engine like behavior to refrigerator like behavior by adjusting the ratio of "up time" to "down time"  properly in each time period. So, by adjusting the pulse waveform properly, "quantum heat engine" can be transformed into "quantum refrigerator" and vice-versa.

Two-level system (TLS), weakly coupled to a thermal bath, can be used "quantum probe" in presence of periodic frequency modulation for precise thermometric measurement of the bath.  We have found that, the relative error in the measurement of temperature of the bath can be made smaller with asymmetric rectangular pulse modulation than that with symmetric square pulse modulation. Thus, asymmetry in the waveform results in precise measurement of low temperature of microscopic objects. This work has been published as Phys. Rev. E 102, 022140 (2020)