Long-Range Entangled-Plaquette States for Critical and Frustrated Quantum Systems on a Lattice

Abstract

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.

arXiv comment14 pages, 14 figures

References in corpus (36)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Spin-lattice coupling in frustrated antiferromagnets
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Computational Studies of Quantum Spin Systems
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Bosonizing one-dimensional cold atomic gases
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Meron-Cluster Solution of Fermion Sign Problems
• Approximating quantum many-body wave-functions using artificial neural networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Numerical and approximate analytical results for the frustrated spin-1/2 quantum spin chain
• Approximating strongly correlated spin and fermion wavefunctions with correlator product states
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Ground-state phase diagram of the quantum J1-J2 model on the honeycomb lattice
• Finite correlation length scaling with infinite projected entangled-pair states
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• Dynamical structure factor of the $J_1-J_2$ Heisenberg model in one dimension: the variational Monte Carlo approach
• Interaction-induced anomalous quantum Hall state on the honeycomb lattice
• Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states
• Mott transition in bosonic systems: Insights from the variational approach
• Capturing long range correlations in two-dimensional quantum lattice systems using correlator product states
• From Luttinger liquid to Mott insulator: the correct low-energy description of the one-dimensional Hubbard model by an unbiased variational approach
• Variational study of a mobile hole in a two dimensional quantum antiferromagnet using entangled-plaquette states
• Incommensurability Effects in Odd Length J_1-J_2 Quantum Spin Chains: On-site magnetization and Entanglement
• Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Time Evolution and Deterministic Optimisation of Correlator Product States

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