arXiv subjects

Erik Lennart Weerda

Publications and source records attributed to Erik Lennart Weerda.

6 recordsLinked to original sources

arXiv2026

An extended non-magnetic phase in the spin-1/2 Heisenberg antiferromagnet from the ruby to the maple-leaf lattice

The spin-1/2 Heisenberg antiferromagnet on the two-dimensional ruby and maple-leaf lattices provides a stringent test case for frustrated quantum magnetism, where semiclassical magnetic order competes closely with quantum-paramagnetic states. We study the generalized maple-leaf model along the axis interpolating between the isotropic ruby lattice and the isotropic maple-leaf lattice, using two independent variational infinite projected entangled-pair state ansätze: one defined on the mapped square lattice and one directly on the native triangular lattice. Our lowest-energy variational states show no magnetic order throughout the region connecting the two isotropic limits, and the local bond correlations recover the $120^\circ$ lattice rotation symmetry without imposing it explicitly. Magnetic-field simulations at the two endpoints further indicate a finite zero-magnetization plateau in both cases, with a gradual onset of magnetization on the ruby lattice and a sharper onset on the maple-leaf lattice. These results establish a broad gapped non-magnetic regime in a minimal nearest-neighbor Heisenberg model on lattices of direct relevance to both frustrated quantum magnets and programmable ruby-lattice simulators.

cond-mat.str-el↗

arXiv2026

Cooper quartets and fractional vortices in frustrated Josephson junction dice arrays

Superconductivity mediated by Cooper quartets of charge 4e is a phenomenon of key importance for both the understanding of certain exotic superconductors and the engineering of quantum memories protected at the hardware level by topological order. Josephson junction arrays in the shape of the dice lattice constitute one of the main candidates for the realization of this phase of matter. Here, we analyze numerical signatures of the emergence of this exotic phase when superconducting dice arrays are frustrated by inserting one third of a flux quantum per rhombic plaquette. We adopt simulations of relaxation dynamics to study the critical current of such devices and analyse the Fourier decomposition of their bulk supercurrents. A further characterization of these systems at finite temperature is obtained through Monte Carlo techniques and two-dimensional infinite tensor networks. Our results indicate that the observed peaks of the critical current and temperature at frustration 1/3 correspond to a superconductor-insulator phase transition compatible with the deconfinement of half-vortices, while the low-temperature correlation functions of the model confirm the onset of a 4e superconducting phase mediated by Cooper quartets. We finally address the effects of Josephson energy and flux disorder typical of experimental arrays, and comment on the role of charging energies in the corresponding two-dimensional quantum model.

cond-mat.mes-hall↗

arXiv2025

Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach

Projected entangled-pair states (PEPS) have become a powerful tool for studying quantum many-body systems in the condensed matter and quantum materials context, particularly with advances in variational energy optimization methods. A key challenge within this framework is the computational cost associated with the contraction of the two-dimensional lattice, crucial for calculating state vector norms and expectation values. The conventional approach, using the corner transfer matrix renormalization group (CTMRG), involves combining two tensor network layers, resulting in significant time and memory demands. In this work, we introduce an alternative "split-CTMRG" algorithm, which maintains separate PEPS layers and leverages new environment tensors, reducing computational complexity while preserving accuracy. Benchmarks on quantum lattice models demonstrate substantial speedups for variational energy optimization, rendering this method valuable for large-scale PEPS simulations.

cond-mat.str-el↗

arXiv2025

Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States

Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this paper, we propose the optimization of PEPS via an improved formulation of the time-dependent variational principle (TDVP), namely the minimum-step stochastic-reconfguration scheme recently introduced for neural quantum states. We further discuss possible numerical issues that might arise in such a sampling-based approach. In this context, investigate the entanglement properties of random PEPS and find an entanglement phase transition. We note that on one side of this transition, we can identify positive random tensors as product states. To demonstrate the power of the framework described in this paper, we apply the PEPS to study the notoriously challenging chiral spin liquids. Moreover, we exhibit our approach's capability to naturally handle long-range interactions by exploring the phase diagram of Rydberg atom arrays with long-range interactions. We further provide parallelized easy-to-use code, allowing the straightforward application of our method to general Hamiltonians composed of local interaction terms.

cond-mat.str-el↗

arXiv2024

An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results.

cond-mat.str-el↗

arXiv2023

Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model

An important class of model Hamiltonians for investigation of topological phases of matter consists of mobile, interacting particles on a lattice subject to a semi-classical gauge field, as exemplified by the bosonic Harper-Hofstadter model. A unique method for investigations of two-dimensional quantum systems are the infinite projected-entangled pair states (iPEPS), as they avoid spurious finite size effects that can alter the phase structure. However, due to no-go theorems in related cases this was often conjectured to be impossible in the past. In this letter, we show that upon variational optimization the infinite projected-entangled pair states can be used to this end, by identifying fractional Hall states in the bosonic Harper-Hofstadter model. The obtained states are characterized by showing exponential decay of bulk correlations, as dictated by a bulk gap, as well as chiral edge modes via the entanglement spectrum.

cond-mat.str-el↗