We study a Yang-Baxter integrable quantum spin-1/2 chain with random interactions. The Hamiltonian is local and involves two- and three-spin interactions with random parameters. We show that the energy eigenstates of the model are never localized and in fact exhibit perfect energy and spin transport at both zero and infinite temperatures. By considering the vicinity of a free fermion point in the model we demonstrate that this behavior persists under deformations that break Yang-Baxter integrability but preserve the free fermion nature of the Hamiltonian. In this case the ballistic behavior can be understood as arising from the correlated nature of the disorder in the model. We conjecture that the model belongs to a broad class of models avoiding localization in 1D.
We study a Yang-Baxter integrable quantum spin-1/2 chain with random interactions. The Hamiltonian is local and involves two- and three-spin interactions with random parameters. We show that the energy eigenstates of the model are never localized and in fact exhibit perfect energy and spin transport at both zero and infinite temperatures. By considering the vicinity of a free fermion point in the model we demonstrate that this behavior persists under deformations that break Yang-Baxter integrability but preserve the free fermion nature of the Hamiltonian. In this case the ballistic behavior can be understood as arising from the correlated nature of the disorder in the model. We conjecture that the model belongs to a broad class of models avoiding localization in 1D.
Anomalous transport in low dimensional spin chains is an intriguing topic that can offer key insights into the interplay of integrability and symmetry in many-body dynamics. Recent studies have shown that spin-spin correlations in spin chains, where integrability is either perfectly preserved or broken by symmetry-preserving interactions, fall in the Kardar-Parisi-Zhang (KPZ) universality class. Similarly, energy transport can show ballistic or diffusive-like behavior. Although such behavior has been studied under equilibrium conditions, no results on nonequilibrium spin transport in classical spin chains has been reported so far. In this work, we investigate both spin and energy transport in classical spin chains (integrable and nonintegrable) when coupled to two reservoirs at two different temperatures/magnetizations. In both the integrable case and the broken-integrability (but spin-symmetry preserving) case, we report anomalous scaling of spin current with system size (J^{s}∝L^{-μ}), with an exponent value that, within error bars, is close to the KPZ universality class value μ≈2/3. On the other hand, it is noteworthy that the energy current remains ballistic (J^{e}∝L^{-η} with η≈0) in the purely integrable case while there is departure from ballistic behavior (η>0) when integrability is broken regardless of spin-symmetry. We also present results on other interesting observables in the nonequilibrium steady state such as the spatial profiles of magnetization and energy, and spin-spin correlations.
We present a general study of a large family of exactly integrable quantum chains with multispin interactions. The exact integrability follows from the algebraic properties of the energy density operators defining the quantum chains. The Hamiltonians are characterized by a parameter $p=1,2,\ensuremath{\cdots}$ related to the number of interacting spins in the multispin interaction. In the general case, the quantum spins are of infinite dimension. In special cases, characterized by the parameter N=2,3,..., the quantum chains describe the dynamics of Z(N) quantum spin chains with open boundary conditions. The simplest case p=1 corresponds to the free fermionic quantum Ising chain (N=2) or the Z(N) free parafermionic quantum chain. The eigenenergies of the quantum chains are given in terms of the roots of special polynomials, and for general values of p the quantum chains are characterized by a free fermionic (N=2) or free parafermionic (N>2) eigenspectrum. The models have a special critical point when all coupling constants are equal. At this point, the ground-state energy is exactly calculated in the bulk limit, and our analytical and numerical analyses indicate that the models belong to universality classes of critical behavior with dynamical critical exponent z=(p+1)/N and specific-heat exponent $\ensuremath{\alpha}=max{0,1\ensuremath{-}(p+1)/N}$.
High-temperature spin transport in integrable quantum spin chains exhibits a rich dynamical phase diagram, including ballistic, superdiffusive, and diffusive regimes. While integrability is known to survive in static and periodically driven systems, its fate in the complete absence of time-translation symmetry, particularly in interacting random quantum circuits, has remained unclear. Here we construct integrable random quantum circuits built from inhomogeneous XXZ R-matrices. Remarkably, integrability is preserved for arbitrary sequences of gate layers, ranging from quasiperiodic to fully random, thereby explicitly breaking both continuous and discrete time-translation symmetry. Using large-scale time-dependent density-matrix renormalization group simulations at infinite temperature and half filling, we map out the resulting spin-transport phase diagram and identify ballistic, superdiffusive, and diffusive regimes controlled by the spectral parameters of the R-matrices. The spatiotemporal structure of spin correlations within each regime depends sensitively on the inhomogeneity, exhibiting spatial asymmetry and sharp peak structures tied to near-degenerate quasiparticle velocities. To account for these findings, we develop a generalized hydrodynamics framework adapted to time-dependent integrable circuits, yielding Euler-scale predictions for correlation functions, Drude weights, and diffusion bounds. This approach identifies the quasiparticles governing transport and quantitatively captures both the scaling exponents and fine structures of the correlation profiles observed numerically. Our results demonstrate that exact Yang-Baxter integrability is compatible with stochastic quantum dynamics and establish generalized hydrodynamics as a predictive framework for transport in time-dependent integrable systems.
Finite-temperature T > 0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is a prominent example of an integrable correlated system. For electronic densities n ≠ 1 (and spin densities m ≠ 0) it is an ideal charge (and spin) conductor, with ballistic charge (and spin) transport for T ⩾ 0. In spite of the fact that it is solvable by the Bethe ansatz, at n = 1 (and m = 0) its T > 0 charge (and spin) transport properties are an issue that remains poorly understood. Here we combine this solution with symmetry and the explicit calculation of current-operator matrix elements between energy eigenstates to show that for on-site repulsion U > 0 and at n = 1 the charge stiffness D η ( T ) vanishes for T > 0 in the thermodynamic limit. A similar behavior is found by such methods for the spin stiffness D s ( T ) for U > 0 and T > 0, which vanishes at m = 0. This absence of finite temperature n = 1 ballistic charge transport and m = 0 ballistic spin transport are exact results that clarify long-standing open problems.
The t-model represents the Hubbard model in the limit U→∞ and is one of the basic models of strongly correlated electrons. On a one-dimensional chain, the model is integrable, and the charge dynamics corresponds to that of free spinless fermions. However, the sequence of spins is frozen, leading to the Hilbert space fragmentation and nontrivial spin dynamics. We consider integrable and perturbed models with perturbations that break integrability while preserving fragmentation, and show that they exhibit various types of spin dynamics, from ballistic transport to anomalous diffusion in the integrable case, and from diffusion to subdiffusion in the perturbed case. Due to fragmentation, in all cases considered, spin transport is mediated by charge transport, with a particular magnetization dependence, most notably leading to subdiffusion in the grandcanonical average of the perturbed model, with a mechanism distinct from subdiffusion in disordered or dipole-conserving models.
We study the effects of quenched disorder in a class of quantum chains with (p+1)-multispin interactions exhibiting a free fermionic spectrum, paying special attention to the case p=2. Depending if disorder couples to (i) all the couplings or just to (ii) some of them, we have two distinct physical scenarios. In case (i), we find that the transitions of the model are governed by a universal infinite-randomness critical point surrounded by quantum Griffiths phases similarly as happens to the random transverse-field Ising chain. In case (ii), we find that quenched disorder becomes an irrelevant perturbation: the clean critical behavior is stable and Griffiths phases are absent. Beyond the perturbative regime, disorder stabilizes a line of finite-randomness critical points (with nonuniversal critical exponents), that ends in a multicritical point of infinite-randomness type. In that case, quantum Griffiths phases also appear surrounding the finite-disorder transition point. We have characterized the correlation functions and the low-temperature thermodynamics of these chains. Our results are derived from a strong-disorder renormalization-group technique and from finite-size scaling analysis of the spectral gap computed exactly (up to sizes $\ensuremath{\sim}{10}^{7}$) via an efficient new numerical method recently introduced in the literature [Phys. Rev. B 104, 174206 (2021)].