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Classifying Yang-Baxter operators is an essential first step in the study of the simulation of integrable quantum systems on quantum computers. One of the earliest initiatives was taken by Hietarinta in classifying constant Yang-Baxter solutions for a two-dimensional local Hilbert space (qubit representation). He obtained 11 families of invertible solutions, including the one generated by the permutation operator. While these methods work well for 4 by 4 solutions, they become cumbersome for higher dimensional representations. In this work, we overcome this restriction by constructing the constant Yang-Baxter solutions in a representation independent manner by using ans\"{a}tze from algebraic structures. We use four different algebraic structures that reproduce 10 of the 11 Hietarinta families when the qubit representation is chosen. The methods include a set of commuting operators, Clifford algebras, Temperley-Lieb algebras, and partition algebras. We do not obtain the $(2,2)$ Hietarinta class with these methods., Comment: 26 pages + References

The centrality measure (CM) is one of the most fundamental metrics for evaluating the efficiency and vulnerability analysis of complex power grids (CPGs). Despite an abundance of different CMs for individual nodes, there are only a few metrics available in the literature to measure the centrality of individual lines. We propose here the current-flow (CF) line CMs to identify the ranking of lines, where each set of lines is associated with a different level of importance. We then find the CMs using effective resistance and apply it to identify the important lines in a commonly used IEEE 118-bus network. Finally, the efficiency and vulnerability of CPG are analyzed to validate the proposed concepts., Comment: None

We propose a construction of kinetically constrained models using the Markovian quantum dynamics under strong dissipation. Engineering the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation through classical noise, we show that strong dissipation leads to the emergent decoherence-free subspaces, within which constrained quantum many-body unitary dynamics can take place. We argue that the unitary dynamics constructed by the GKSL dynamics is more tightly constrained than that constructed by the strongly interacting Hamiltonian, where the interactions have the same form with the GKSL jump operators. As an example, we demonstrate that a one-dimensional spin system with two-site dissipation leads to the kinetically constrained "PXQ" model, which exhibits the free domain-wall motion with an additional frozen-block structure. Under a uniform magnetic field, the PXQ model shows the domain-wall localization, similar to the Wannier-Stark localization. We then couple two PXQ chains with the magnetic field by an inter-chain interaction. We discover that, while localization of the domain walls persists despite the interactions for typical parameter regimes, a non-trivial partial delocalization appears for a certain parameter line., Comment: 18 pages, 8 figures. Published version

A crossover between different power-law relaxation behaviors of many-body periodically driven integrable systems has come to light in recent years. We demonstrate using integrable quantum systems, that similar kinds of dynamical transitions may also occur in the relaxation of such systems following a sudden quench. Particularly, we observe two distinct power-law relaxation behaviors following a sudden quench in the integrable XY model, depending upon whether the quenched Hamiltonian lies in the commensurate or the incommensurate phase. The relaxation behavior for quenches at and near the boundary line, called the disorder line (DL), separating these phases is also characterized. The relaxation at the DL shows a new scaling exponent previously unexplored. The transitions occur through a crossover from the commensurate/incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges like a power law as the parameters of the final quenched Hamiltonian approach the DL. The transitions are also observed to be robust under weak integrability breaking perturbations but disappear following strongly chaotic quenches., Comment: 14 pages, 14 figures

We study the temporal evolution of the mutual information (MI) in a one-dimensional Kitaev chain, coupled to a fermionic Markovian bath, subsequent to a global quench of the chemical potential. In the unitary case, the MI (or equivalently the bipartite entanglement entropy) saturates to a steady-state value (obeying a volume law) following a ballistic growth. On the contrary, we establish that in the dissipative case the MI is exponentially damped both during the initial ballistic growth as well as in the approach to the steady state. We observe that even in a dissipative system, postquench information propagates solely through entangled pairs of quasiparticles having a finite lifetime; this quasiparticle picture is further corroborated by the out-of-equilibrium analysis of two-point fermionic correlations. Remarkably, in spite of the finite lifetime of the quasiparticles, a finite steady-state value of the MI survives in asymptotic times which is an artifact of nonvanishing two-point correlations. Further, the finite lifetime of quasiparticles renders to a finite length scale in these steady-state correlations., Comment: 6+7 pages, 3+5 figures, accepted for publication in PRB(R)

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., Comment: 23 pages, 9 figures; Topical Review article; Published version

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 non-commuting Hamiltonians. In the high frequency limit $\omega \to \infty$, we show that the system reaches a non-equilibrium 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., Comment: 16 pages, 5 figures; added a discusion of the behavior of the system over very long times; this is the published version

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 $1/l^{\alpha}$, where $l$ is the distance between the two sites and $\alpha$ is a positive constant. Considering very large system sizes, we show that when $\alpha >1$, 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 $\alpha <1$, there exist symmetry protected massive Dirac end modes. We further study the dynamical phase boundary of the model when periodic $\delta$-function kicks are applied to the chemical potential; we specially focus on the case $\alpha >1$ and analyze the corresponding Floquet quasienergies. Interestingly, we find that new topologically protected massless end modes are generated at the quasienergy $\pi/T$ (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 $\pi/T$ for a periodically kicked system with $\alpha > 1$., Comment: 15 pages, 8 figures

We investigate the dynamics of two Jordan Wigner solvable models, namely, the one dimensional chain of hard-core bosons (HCB) and the one-dimensional transverse field Ising model under coin-toss like aperiodically driven staggered on-site potential and the transverse field, respectively. It is demonstrated that both the models heat up to the infinite temperature ensemble for a minimal aperiodicity in driving. Consequently, in the case of the HCB chain, we show that the initial current generated by the application of a twist vanishes in the asymptotic limit for any driving frequency. For the transverse Ising chain, we establish that the system not only reaches the diagonal ensemble but the entanglement also attains the thermal value in the asymptotic limit following initial ballistic growth. All these findings, contrasted with that of the perfectly periodic situation, are analytically established in the asymptotic limit within an exact disorder matrix formalism developed using the uncorrelated binary nature of the coin-toss aperiodicity., Comment: 13 pages, 4 figures

We study an integrable Hamiltonian reducible to free fermions which is subjected to an imperfect periodic driving with the amplitude of driving (or kicking) randomly chosen from a binary distribution like a coin-toss problem. The randomness present in the driving protocol destabilises the periodic steady state, reached in the limit of perfectly periodic driving, leading to a monotonic rise of the stroboscopic residual energy with the number of periods ($N$). We establish that a minimal deviation from the perfectly periodic driving would always result in a {\it bounded} heating up of the system with $N$ to an asymptotic finite value. Remarkably, exploiting the completely uncorrelated nature of the randomness and the knowledge of the stroboscopic Floquet operator in the perfectly periodic situation, we provide an exact analytical formalism to derive the disorder averaged expectation value of the residual energy through a {\it disorder operator}. This formalism not only leads to an immense numerical simplification, but also enables us to derive an exact analytical form for the residual energy in the asymptotic limit which is universal, i.e, independent of the bias of coin-toss and the protocol chosen. Furthermore, this formalism clearly establishes the nature of the monotonic growth of the residual energy at intermediate $N$ while clearly revealing the possible non-universal behaviour of the same., Comment: 14 pages, 5 figures