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Register a new userQuantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions
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For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several truncations of the time evolution equations up to eighth order in the Jordan-Wigner fermionic operators. The resulting set of differential equations can be solved for lattices with $O(10^2)$ sites and facilitates the computation of spin expectation values and correlation functions to high accuracy, at least for moderate timescales. We use this scheme to study the relaxation dynamics of the model, involving prethermalisation and thermalisation. The techniques developed here can be generalised to other spin models with weak integrability-breaking terms.
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In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body physics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform martrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. textit{Anomalous} cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, textit{regular} cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups, and we outline the associated experimental considerations.
Using an infinite Matrix Product State (iMPS) technique based on the time-dependent variational principle (TDVP), we study two major types of dynamical phase transitions (DPT) in the one-dimensional transverse-field Ising model (TFIM) with long-range power-law ($propto1/r^{alpha}$ with $r$ inter-spin distance) interactions out of equilibrium in the thermodynamic limit -- textit{DPT-I}: based on an order parameter in a (quasi-)steady state, and textit{DPT-II}: based on non-analyticities (cusps) in the Loschmidt-echo return rate. We construct the corresponding rich dynamical phase diagram, whilst considering different quench initial conditions. We find a nontrivial connection between both types of DPT based on their critical lines. Moreover, and very interestingly, we detect a new DPT-II dynamical phase in a certain range of interaction exponent $alpha$, characterized by what we call textit{anomalous cusps} that are distinct from the textit{regular cusps} usually associated with DPT-II. Our results provide the characterization of experimentally accessible signatures of the dynamical phases studied in this work.
We state and prove four types of Lieb-Robinson bounds valid for many-body open quantum systems with power law decaying interactions undergoing out of equilibrium dynamics. We also provide an introductory and self-contained discussion of the setting and tools necessary to prove these results. The results found here apply to physical systems in which both long-ranged interactions and dissipation are present, as commonly encountered in certain quantum simulators, such as Rydberg systems or Coulomb crystals formed by ions.
Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s=1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as log(n)/2 + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.
In this study, considering the long-range interaction with an inverse-square and its trigonometric and hyperbolic variants in SCM model we investigate entanglement in (1/2,1) mixed-spin XY model. We also discuss the temperature and magnetic field dependence of the thermal entanglement in this system for different types of interaction. The numerical results show that, in the presence of the long-range interactions, thermal entanglement between spins has a rich behavior dependent upon the interaction strength, temperature and magnetic field. Indeed we find that for less than a critical distance there are entanglement plateaus dependent upon the distance between the spins, whereas above the critical distance the entanglement can exhibit sudden death.
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