We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under "twisted" translations, combining an ordinary translation with a spin flip at one end of the chain. It includes a remarkable model with elliptic spin-spin interactions, smoothly interpolating between the XXX Heisenberg model with anti-periodic boundary conditions and a new open chain with sites uniformly spaced on a half-circle and interactions inversely proportional to the square of the distance between the spins. We are able to compute in closed form the partition function of the latter chain, thereby obtaining a complete description of its spectrum in terms of a pair of independent su(1|1) and ${\rm su}(m/2)$ motifs when the number $m$ of internal degrees of freedom is even. This implies that the even $m$ model is invariant under the direct sum of the Yangians $Y$(gl(1|1)) and $Y$(gl$(0|m/2)$). We also analyze several statistical properties of the new chain's spectrum. In particular, we show that it is highly degenerate, which strongly suggests the existence of an underlying (twisted) Yangian symmetry also for odd $m$.
It is shown that as far as the linear diffusion equation meets both time- and space- translational invariance, the time dependence of a moment of degree $α$ is a polynomial of degree at most equal to $α$, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.
Investigating translationally invariant qudit spin chains with a low local dimension, we ask what is the best possible tradeoff between the scaling of the entanglement entropy of a large block and the inverse-polynomial scaling of the spectral gap. Restricting ourselves to Hamiltonians with a "rewriting" interaction, we find the pair-flip model, a family of spin chains with nearest neighbor, translationally invariant, frustration-free interactions, with a very entangled ground state and an inverse-polynomial spectral gap. For a ground state in a particular invariant subspace, the entanglement …
In this paper we study one-dimensional quantum Ising spin chains in external magnetic field close to an integrable point. We concentrate on the dynamics of the slowest operator, that plays a key role at the final period of thermalization. We introduce two independent definitions of the slowest operator: local and translationally-invariant ones. We construct both operators numerically using tensor networks and extensively compare their physical properties. We find that the local operator has a significant overlap with energy flux, it does not correspond to an integral of motion, and, as one goe…
We investigate transport in several translationally invariant spin-1/2 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous non-equilibrium density and the current auto-correlation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows …
We study the conditions under which one can conserve local translationally invariant operators by local translationally invariant Lindblad equations in one-dimensional rings of spin-1/2 particles. We prove that for any 1-local operator (e.g., particle density) there exist Lindblad dissipators that conserve that operator, while on the other hand we prove that among 2-local operators (e.g., energy density) only trivial ones of the Ising type can be conserved, while all the other cannot be conserved, neither locally nor globally, by any 2- or 3-local translationally invariant Lindblad equation. O…
We recently showed [Phys. Rev. Lett. 121, 220602 (2018)] that the average bipartite entanglement entropy of all energy eigenstates of the quantum Ising chain exhibits a universal (for translationally invariant quadratic fermionic models) leading term that scales linearly with the subsystem's volume, while in the thermodynamic limit the first subleading correction does not vanish at the critical field (it only depends on the ratio $f$ between the volume of the subsystem and volume of the system) and vanishes otherwise. Here we show, analytically for bounds and numerically for averages, that the…
Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are universal: they can replicate -- in a precise and rigorous sense -- the complete physics of any other classical spin model, to any desired accuracy. However, all previously known universal models break translational invariance. In this paper we show that there exist translationally invariant universal models. Our main result is an explicit construction of a tra…
We numerically construct translationally invariant quasi-conserved operators with maximum range M which best-commute with a non-integrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasi-conserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasi-conserved operator can be understood as a dressed total "spin-z" operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same…
We show that long-range ferromagnetic interactions in quantum spin chains can induce spatial quasi-localization of topological magnetic defects, i.e., domain-walls, even in the absence of quenched disorder. By means of matrix-product-states numerical techniques, we study the non-equilibrium evolution of initial states with one or more domain-walls under the effect of a transverse field in variable-range quantum Ising chains. Upon increasing the range of these interactions, we demonstrate the occurrence of a sharp transition characterized by the suppression of spatial diffusion of the magnetic …
We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We prove that, for open boundary conditions, the model exhibits no finite-temperature phase transition. Yet we find that it displays glassy dynamics with astronomically slow relaxation times, numerically consistent with a double exponential dependence on the inverse temperature. The slowness of the dynamics arises due to errors that occur during thermal annealin…
We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the walls become important. We provide a simple and general formula for the effective diffusion constant along the channel as well as the first non-trivial finite time correction for arbitrary flows along the channel, arbitrary interaction potentials with the walls and arbitrary expressions for the diffusion tensor. The formula are in particular amenable to a str…
We discuss a general mean field plus random phase approximation (RPA) for describing composite systems at zero and finite temperature. We analyze in particular its implementation in finite systems invariant under translations, where for uniform mean fields it requires just the solution of simple local-type RPA equations. As test and application, we use the method for evaluating the entanglement between two spins in cyclic spin 1/2 chains with both long and short range anisotropic XY-type couplings in a uniform transverse magnetic field. The approach is shown to provide an accurate analytic des…
The ground state and thermodynamics of a generalized spin-1/2 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins are calculated exactly using the mapping method based on the decoration-iteration transformation. Rigorous results for the magnetization, susceptibility, and heat capacity are investigated in dependence on temperature and magnetic field for the frustrated diamond spin chain with the antiferromagnetic Ising and Heisenberg interactions. It is demonstrated that the second-neighbor interaction between nodal spins gives rise to a greater diversity of …
We consider a quench in an infinite spin ladder describing a system with two species of bosons in the limit of strong interactions. If the heavy bosonic species has infinite mass the model becomes a spin chain with quenched binary disorder which shows true Anderson localization (AL) or many-body localization (MBL). For finite hopping amplitude $J'$ of the heavy particles, on the other hand, we find an exponential polarization decay with a relaxation rate which depends monotonically on $J'$. Furthermore, the entanglement entropy changes from a constant (AL) or logarithmic (MBL) scaling in time …
We discuss a notion of quantum critical exponents in open quantum many-body systems driven by quantum noise. We show that in translationally invariant quantum lattice models undergoing quasi-local Markovian dissipative processes, mixed states emerge as stationary points that show scaling laws for the divergence of correlation lengths giving rise to well-defined critical exponents. The main new technical tool developed here is a complete description of steady states of free bosonic or fermionic translationally invariant systems driven by quantum noise: This approach allows to express all correl…
We consider the isotropic spin-1/2 Heisenberg spin chain weakly perturbed by a local translationally- and SU(2)-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-conserved integrals of motion (charges) for the perturbed model. Such quasi-conserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation only the first few integrals of motion can be promoted to the quasi-conserved charges, whereas hig…
We investigate the entanglement and nonlocality properties of two random XX spin-1/2 critical chains, in order to better understand the role of breaking translational invariance to achieve nonlocal states in critical systems. We show that breaking translational invariance is a necessary but not sufficient condition for nonlocality, as the random chains remain in a local ground state up to a small degree of randomness. Furthermore, we demonstrate that the random dimer model does not have the same nonlocality properties of the translationally invariant chain, even though they share the same univ…
The spin-1 Ising-Heisenberg diamond chain in a magnetic field is exactly solved by a rigorous treatment based on the transfer-matrix method. An exact ground-state phase diagram includes in total three unconventional quantum ground states with a quantum entanglement of the decorating spin-1 Heisenberg dimers apart from two ground states with a classical spin arrangement. It is evidenced that all three values of the magnetization allowed for the spin-1 diamond chain without translationally broken symmetry by the Oshikawa-Yamanaka-Affleck criterion can become evident in an outstanding stepwise ma…
We consider the translationally invariant but parity (left-right symmetry) breaking Ising chain Hamiltonian \begin{equation} {\cal H} = -U_2\sum_{k} s_{k}s_{k+1} - U_3\sum_{k} s_{k}s_{k+1}s_{k+3} \nonumber \end{equation} and let this system evolve by Kawasaki spin exchange dynamics. Monte Carlo simulations show that perturbations forcing this system off equilibrium make it act as a Brownian molecular motor which, in the lattice gas interpretation, transports particles along the chain. We determine the particle current under various different circumstances, in particular as a function of the ra…
We investigate ground- and excited-state properties of the deformed Fredkin spin chain proposed by Salberger, Zhang, Klich, Korepin, and the authors. This model is a one-parameter deformation of the Fredkin spin chain, whose Hamiltonian is $3$-local and translationally invariant in the bulk. The model is frustration-free and its unique ground state can be expressed as a weighted superposition of colored Dyck paths. We focus on the case where the deformation parameter $t>1$. By using a variational method, we prove that the finite-size gap decays at least exponentially with increasing the system…
The spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between the nodal spins is rigorously solved using the transfer-matrix method. Exact results for the ground state, magnetization process and specific heat are presented and discussed in particular. It is shown that the further-neighbor interaction between the nodal spins gives rise to three novel ground states with a translationally broken symmetry, but at the same time, it does not increases the total number of intermediate plateaus in a zero-temperature magnetization curve compared with the simplified model withou…
We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and construct a general, self-contained theory of ground state factorization in frustration free quantum spin models defined on lattices in any spatial dimension and for interactions of arbitrary range. We show that, quite generally, non exactly solvable translationally invariant models in presence of an external uniform magnetic field can admit exact, fully factor…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of Östlund and Rommer [1], we separate the Hilbert space of the system into subspaces with different momentum. This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation. Surprisingly, many branches of the dispersion relation are approximated to a ve…
We introduce the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains, criticality is accompanied with the possibility of distilling a maximally entangled state of arbitrary dimension from a sufficiently large block deterministically, with local operations and classical communication. These analytical results -- which refine previous results on the divergence of block entropy as the rate at which EPR pairs can be distilled from many…
We construct a hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples N transverse field Ising chains such that the resulting theory is critical and described by the so(N)_1 conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary N into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. F…
Spin-1/2 orthogonal-dimer chain composed of regularly alternating Ising and Heisenberg dimers is exactly solved in a presence of the magnetic field by the transfer-matrix method. It is shown that the ground-state phase diagram involves in total six different phases. Besides the ferromagnetic phase with fully polarized spins one encounters the singlet antiferromagnetic and modulated antiferromagnetic phases manifested in zero-temperature magnetization curves as zero magnetization plateau, the frustrated ferrimagnetic and singlet ferrimagnetic phases causing existence of an intermediate one-half…
