Heat Conductivity of the Heisenberg Spin-1/2 Ladder: From Weak to Strong Breaking of Integrability

Anomalous transport from hot quasiparticles in interacting spin chains

Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.

Approaching the isotropic spin-ladder regime: structure and magnetism of all-pyrazine-bridged copper(II)-based antiferromagnetic ladders

The crystal structure and magnetic properties of two all-pyrazine-bridged antiferromagnetic spin ladders are reported. The complexes, catena-(bis(3-X-4-pyridone)(μ-pyrazine)copper(II)(-μ-pyrazine)diperchlorate ([Cu(pz)_1.5(L)₂](ClO₄)₂ where L = 3-X-4-pyridone and X = Br (1) or Cl (2)), contain copper(II)-based ladders in which both the rung and rail bridges are pyrazine molecules bonded through the x²-y² orbital of the copper(II) ions. This structural scaffold is proposed to approach the isotropic spin-ladder regime. 1 and 2 crystallize in the monoclinic space group P2₁/c. Due to the bulk of the 3-X-4-HOpy ligands, the ladders are well isolated in the a-direction (1, 15.6 Å; 2, 15.5 Å). The ladders, which run in the b-direction, are stacked in the c-direction with the separation (1, 7.87 Å; 2, 7.82 Å) between copper(II) ions caused by the bulk of a semi-coordinate perchlorate ion coordinated in the axial position. Computational evaluation of magnetic J_AB couplings between Cu-moieties of 2 supports the experimentally proposed magnetic topology and agrees with an isolated isotropic spin-ladder (J_rail = -4.04 cm^-1 (-5.77 K) and J_rung = -3.89 cm^-1 (-5.56 K)). These complexes introduce a convenient scaffold for synthesizing isotropic spin-ladders with modest superexchange interactions, the strength of which may be tuned by variations in L. The magnetic susceptibility down to 1.8 K, for both compounds, is well described by the strong-rung ladder model giving nearly isotropic exchange with J_rung ≈ J_rail ≈ -5.5 K (1) and -5.9 K (2) using the Hamiltonian. Theoretical simulations of the magnetic response of 2 using the isotropic ladder model are in excellent agreement with experiment. The measured magnetization to 5 T indicates a quantum-dominated magnetic spectrum. Again, calculated lower and saturation (4.3 and 24 T, respectively) critical fields for 2 are consistent with experimental measurements, and magnetization data at very low temperatures indeed suggest the presence of quantum effects. Further, the computational study of short- and long-range spin ordering indicates that a 2D-to-3D crossover might be feasible at lower temperatures. Analysis of the Boltzmann population corroborates the presence of accessible triplet states above the singlet ground state enabling the aforementioned 2D-to-3D crossover.

Nontrivial damping of quantum many-body dynamics

Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schrödinger picture. We show that a nontrivial damping in the Schrödinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.

Weak Integrability Breaking: Chaos with Integrability Signature in Coherent Diffusion

We study how perturbations affect dynamics of integrable many-body quantum systems, causing transition from integrability to chaos. Looking at spin transport in the Heisenberg chain with impurities we find that in the thermodynamic limit transport gets diffusive already at an infinitesimal perturbation. Small extensive perturbations therefore cause an immediate transition from integrability to chaos. Nevertheless, there is a remnant of integrability encoded in the dependence of the diffusion constant on the impurity density, namely, at small densities it is proportional to the square root of the inverse density, instead of to the inverse density as would follow from Matthiessen's rule. We show that Matthiessen's rule has to be modified in nonballistic systems. Results also highlight a nontrivial role of interacting scattering on a single impurity, and that there is a regime where adding more impurities can actually increase transport.

Exponential damping induced by random and realistic perturbations

Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that if the perturbation exhibits a random-matrix structure in the eigenbasis of the unperturbed Hamiltonian, then this perturbation effectively leads to an exponential damping of the original dynamics. Employing a combination of dynamical quantum typicality and numerical linked cluster expansions, we demonstrate that our theoretical findings for random matrices can, in some cases, be relevant for the dynamics of realistic quantum many-body models as well. Specifically, we study the decay of current autocorrelation functions in spin-1/2 ladder systems, where the rungs of the ladder are treated as a perturbation to the otherwise uncoupled legs. We find a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.

Selected applications of typicality to real-time dynamics of quantum many-body systems

Loosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the dynamics of quantum many-body systems, called dynamical quantum typicality (DQT). In this paper, we give a brief overview of selected applications of DQT, where particular emphasis is given to questions on transport and thermalization in low-dimensional lattice systems like chains or ladders of interacting spins or fermions. For these systems, we discuss that DQT provides an efficient means to obtain time-dependent equilibrium correlation functions for comparatively large Hilbert-space dimensions and long time scales, allowing the quantitative extraction of transport coefficients within the framework of, e. g., linear response theory (LRT). Furthermore, it is discussed that DQT can also be used to study the far-from-equilibrium dynamics resulting from sudden quench scenarios, where the initial state is a thermal Gibbs state of the pre-quench Hamiltonian. Eventually, we summarize a few combinations of DQT with other approaches such as numerical linked cluster expansions or projection operator techniques. In this way, we demonstrate the versatility of DQT.

Magnetic-Order Crossover in Coupled Spin Ladders

We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-1/2 Heisenberg antiferromagnetic ladder compound (C_{7}H_{10}N)_{2}CuBr_{4}. The staggered order was previously evidenced from a continuous and symmetric splitting of ^{14}N NMR spectral lines on lowering the temperature below T_{c}≃330  mK, with a saturation towards ≃150  mK. Unexpectedly, the split lines begin to further separate away below T^{*}∼100  mK, while the linewidth and the line shape remain completely invariable. This crossover behavior is further corroborated by the NMR relaxation rate T_{1}^{-1} measurements. A very strong suppression reflecting the ordering, T_{1}^{-1}∼T^{5.5}, observed above T^{*}, is replaced by T_{1}^{-1}∼T below T^{*}. These original NMR features are indicative of the unconventional nature of the crossover, which may arise from a unique arrangement of the ladders into a spatially anisotropic and frustrated coupling network.

Eigenstate thermalization hypothesis and quantum Jarzynski relation for pure initial states

Since the first suggestion of the Jarzynski equality many derivations of this equality have been presented in both the classical and the quantum context. While the approaches and settings differ greatly from one another, they all appear to rely on the condition that the initial state is a thermal Gibbs state. Here, we present an investigation of work distributions in driven isolated quantum systems, starting from pure states that are close to energy eigenstates of the initial Hamiltonian. We find that, for the nonintegrable quantum ladder studied, the Jarzynski equality is fulfilled to a good accuracy.