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Register a new userBound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
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We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.
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We analyze and discuss convergence properties of a numerically exact algorithm tailored to study the dynamics of interacting two-dimensional lattice systems. The method is based on the application of the time-dependent variational principle in a manifold of binary and quaternary Tree Tensor Network States. The approach is found to be competitive with existing matrix product state approaches. We discuss issues related to the convergence of the method, which could be relevant to a broader set of numerical techniques used for the study of two-dimensional systems.
We explore a variational Ansatz for lattice quantum systems -- named long-range entangled-plaquette state -- in which pairs of clusters of adjacent lattice sites are correlated at any distance. The explicit scale-free structure of correlations built in this wave function makes it fit to reproduce critical states with long-range entanglement. The use of complex weights in the Ansatz allows for an efficient optimization of non positive definite states in a fully variational fashion, namely without any additional bias (arising emph{e.g.} from pre-imposed sign structures) beyond that imposed by the parametrization of the state coefficients. These two features render the Ansatz particularly appropriate for the study of quantum phase transitions in frustrated systems. Moreover, the Ansatz can be systematically improved by increasing the long range plaquette size, as well as by the inclusion of even larger adjacent-site plaquettes. We validate our Ansatz in the case of the XX and Heisenberg chain, and further apply it to the case of a simple, yet paradigmatic model of frustration, namely the $J_1-J_2$ antiferromagnetic Heisenberg chain. For this model we provide clear evidence that our trial wave function faithfully describes both the short-range physics (particularly in terms of ground state energy) and the long-range one expressed by the Luttinger exponent, and the central charge of the related conformal field theory, which govern the decay of correlations and the scaling of the entanglement entropy, respectively. Finally we successfully reproduce the incommensurate correlations developing in the system at strong frustration, as a result of the flexible representation of sign (phase) structures via complex weights.
We study the quantum phase transitions in the two-dimensional spin-orbit models in terms of fidelity susceptibility and reduced fidelity susceptibility. An order-to-order phase transition is identified by fidelity susceptibility in the two-dimensional Heisenberg XXZ model with Dzyaloshinsky-Moriya interaction on a square lattice. The finite size scaling of fidelity susceptibility shows a power-law divergence at criticality, which indicates the quantum phase transition is of second order. Two distinct types of quantum phase transitions are witnessed by fidelity susceptibility in Kitaev-Heisenberg model on a hexagonal lattice. We exploit the symmetry of two-dimensional quantum compass model, and obtain a simple analytic expression of reduced fidelity susceptibility. Compared with the derivative of ground-state energy, the fidelity susceptibility is a bit more sensitive to phase transition. The violation of power-law behavior for the scaling of reduced fidelity susceptibility at criticality suggests that the quantum phase transition belongs to a first-order transition. We conclude that fidelity susceptibility and reduced fidelity susceptibility show great advantage to characterize diverse quantum phase transitions in spin-orbit models.
We study a family of frustrated anti-ferromagnetic spin-$S$ systems with a fully dimerized ground state. This state can be exactly obtained without the need to include any additional three-body interaction in the model. The simplest members of the family can be used as a building block to generate more complex geometries like spin tubes with a fully dimerized ground state. After present some numerical results about the phase diagram of these systems, we show that the ground state is robust against the inclusion of weak disorder in the couplings as well as several kinds of perturbations, allowing to study some other interesting models as a perturbative expansion of the exact one. A discussion on how to determine the dimerization region in terms of quantum information estimators is also presented. Finally, we explore the relation of these results with a the case of the a 4-leg spin tube which recently was proposed as the model for the description of the compound Cu$_2$Cl$_4$D$_8$C$_4$SO$_2$, delimiting the region of the parameter space where this model presents dimerization in its ground state.
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin-1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.
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