Relaxation Exponents of OTOCs and Overlap with Local Hamiltonians.

OTOC has been used to characterize the information scrambling in quantum systems. Recent studies have shown that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In particular, the slow scrambling of OTOC is seen for observables that have an overlap with local conserved quantities. However, an observable may not overlap with the Hamiltonian but instead with the Hamiltonian elevated to an exponent larger than one. Here, we show that higher exponents correspond to faster relaxation, although still algebraic, and such exponents can increase indefinitely. Our analytical results are supported by numerical experiments.

Giant Spin Current Rectification Due to the Interplay of Negative Differential Conductance and a Non-Uniform Magnetic Field.

In XXZ chains with large enough interactions, spin transport can be significantly suppressed when the bias of the dissipative driving becomes large enough. This phenomenon of negative differential conductance is caused by the formation of two oppositely polarized ferromagnetic domains at the edges of the chain. Here, we show that this many-body effect, combined with a non-uniform magnetic field, can allow for a high degree of control of the spin current. In particular, by studying all of the possible shapes of local magnetic fields potentials, we find that a configuration in which the magnetic field points up for half of the chain and down for the other half, can result in giant spin-current rectification, for example, up to 108 for a system with only 8 spins. Our results show clear indications that the rectification can increase with the system size.

Energy Current Rectification and Mobility Edges.

We investigate how the presence of a single-particle mobility edge in a system can generate strong energy current rectification. Specifically, we study a quadratic bosonic chain subject to a quasiperiodic potential and coupled at its boundaries to spin baths of differing temperature. We find that rectification increases by orders of magnitude depending on the spatial position in the chain of localized eigenstates above the mobility edge. The largest enhancements occur when the coupling of one bath to the system is dominated by a localized eigenstate, while the other bath couples to numerous delocalized eigenstates. By tuning the parameters of the quasiperiodic potential it is thus possible to vary the amplitude, and even invert the direction, of the rectification.

Transport and Energetic Properties of a Ring of Interacting Spins Coupled to Heat Baths.

We study the heat and spin transport properties in a ring of interacting spins coupled to heat baths at different temperatures. We show that interactions, by inducing avoided crossings, can be a means to tune both the total heat current flowing between the ring and the baths, and the way it flows through the system. In particular, we recognize three regimes in which the heat current flows clockwise, counterclockwise, and in parallel. The temperature bias between the baths also induces a spin current within the ring, whose direction and magnitude can be tuned by the interaction. Lastly, we show how the ergotropy of the nonequilibrium steady state can increase significantly near the avoided crossings.

Perfect Diode in Quantum Spin Chains.

We study the rectification of the spin current in XXZ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 10^{4}) is attainable even using a short chain of N=8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.

Complexity of spin configuration dynamics due to unitary evolution and periodic projective measurements.

We study the Hamiltonian dynamics of a many-body quantum system subjected to periodic projective measurements, which leads to probabilistic cellular automata dynamics. Given a sequence of measured values, we characterize their dynamics by performing a principal component analysis (PCA). The number of principal components required for an almost complete description of the system, which is a measure of complexity we refer to as PCA complexity, is studied as a function of the Hamiltonian parameters and measurement intervals. We consider different Hamiltonians that describe interacting, noninteracting, integrable, and nonintegrable systems, including random local Hamiltonians and translational invariant random local Hamiltonians. In all these scenarios, we find that the PCA complexity grows rapidly in time before approaching a plateau. The dynamics of the PCA complexity can vary quantitatively and qualitatively as a function of the Hamiltonian parameters and measurement protocol. Importantly, the dynamics of PCA complexity present behavior that is considerably less sensitive to the specific system parameters for models which lack simple local dynamics, as is often the case in nonintegrable models. In particular, we point out a figure of merit that considers the local dynamics and the measurement direction to predict the sensitivity of the PCA complexity dynamics to the system parameters.

Transport and spectral properties of the XX+XXZ diode and stability to dephasing.

We study the transport and spectral property of a segmented diode formed by an XX+XXZ spin chain. This system has been shown to become an ideal rectifier for spin current for large enough anisotropy. Here we show numerical evidence that the system in reverse bias has signatures pointing toward the existence of three different transport regimes depending on the value of the anisotropy: ballistic, diffusive, and insulating. In forward bias we observe two regimes, ballistic and diffusive. The system in forward and reverse bias shows significantly different spectral properties, with distribution of rapidities converging toward different functions. In the presence of dephasing the system becomes diffusive, rectification is significantly reduced, the relaxation gap increases, and the spectral properties in forward and reverse bias tend to converge. For large dephasing the relaxation gap decreases again as a result of quantum Zeno physics.

Giant rectification in segmented, strongly interacting spin chains despite the presence of perturbations.

Balachandran et al. [Phys. Rev. Lett. 120, 200603 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.200603] presented a segmented XXZ spin chain with zero anisotropy in one half and a large anisotropy on the other half that gave rise to a spin current rectification which is perfect in the thermodynamic limit. Here we extend the previous study to segmented chains with interacting integrable as well as nonintegrable halves, considering even cases in which no ballistic transport can emerge in either half. We demonstrate that, also in this more general case, it is possible to obtain giant rectification when the two interacting half chains are sufficiently different. We also show that the mechanism causing this effect is the emergence of an energy gap in the excitation spectrum of the out-of-equilibrium insulating steady state in one of the two biases. Finally, we demonstrate that in the thermodynamic limit there is no perfect rectification when each of the two half chains is interacting.

Steady-state quantum transport through an anharmonic oscillator strongly coupled to two heat reservoirs.

We investigate the transport properties of an anharmonic oscillator, modeled by a single-site Bose-Hubbard model, coupled to two different thermal baths using the numerically exact thermofield based chain-mapping matrix product states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the nonequilibrium dynamics of strongly interacting system irrespective of the system-bath coupling against the global master equation approach in Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site interactions, temperature bias as well as the system-bath couplings on the steady-state transport properties. Last, we also show evidence of non-Markovian dynamics by studying the nonmonotonicity of the time evolution of the trace distance between two different initial states.

Heat current rectification in segmented XXZ chains.

We study the rectification of heat current in an XXZ chain segmented in two parts. We model the effect of the environment with Lindblad heat baths. We show that in our system, rectification is large for strong interactions in half of the chain and if one bath is at a cold enough temperature. For the numerically accessible chain lengths, we observe that the rectification increases with the system size. We gain insight into the rectification mechanism by studying two-time correlations in the steady state. The presence of interactions also induces a strong nonlinear response to the temperature difference, resulting in superlinear and negative differential conductance regimes.

Phase-space characterization of complexity in quantum many-body dynamics.

We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well-known measure of complexity in classical systems and which is valid for both pure and mixed states in single-particle and many-body systems, takes into account the combined role of chaos and entanglement in the realm of quantum mechanics. The effectiveness of the measure is illustrated in the example of the Ising chain in a homogeneous tilted magnetic field. We provide numerical evidence that the multipartite entanglement generation leads to a linear increase in entropy until saturation in both integrable and chaotic regimes, so that in both cases the number of harmonics of the Wigner function grows exponentially with time. The entropy growth rate can be used to detect quantum phase transitions. The proposed entropy measure can also distinguish between integrable and chaotic many-body dynamics by means of the size of long-term fluctuations which become smaller when quantum chaos sets in.