arXiv subjects

Pascal M. Vecsei

Publications and source records attributed to Pascal M. Vecsei.

6 recordsLinked to original sources

arXiv2025

Quantum circuit algorithm for topological invariants of second order topological many-body quantum magnets

Topological quantum matter represents a flexible playground to engineer unconventional excitations. While non-interacting topological single-particle systems have been studied in detail, topology in quantum many-body systems remains an open problem. Specifically, in the quantum many-body limit, one of the challenges lies in the computational complexity of obtaining the many-body ground state and its many-body topological invariant. While algorithms to compute ground states with quantum computers have been heavily investigated, algorithms to compute topological invariants in a quantum computer are still under active development. Here we demonstrate a quantum circuit to compute the many-body topological invariant of a second-order topological quantum magnet encoded in qubits. Our algorithm relies on a quantum circuit adiabatic evolution in transverse paths in parameter space, and we uncover hidden topological invariants depending on the traversed path. Our work puts forward an algorithm to leverage quantum computers to characterize many-body topological quantum matter.

quant-ph↗

arXiv2024

Lee-Yang formalism for phase transitions of interacting fermions using tensor networks

Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and unconventional superconductors, that often compete with other symmetry broken states including ordered magnets and charge density waves. Here, we put forward a formalism for determining the phase diagram of fermionic systems that combines recent progress in the field of Lee-Yang theory of phase transitions with many-body tensor-network methods. Using this strategy, we map out the phase diagram of a fermionic chain, where charge density waves form owing to strong repulsion. Specifically, from the high cumulants of the order parameter, we extract the dominant zeros of the moment-generating function in chains of finite size. By extrapolating their positions to the thermodynamic limit, we determine the boundaries between competing phases. Our formalism provides a strategy for determining critical points in fermionic systems, and it is based on fluctuations of the order parameter, which are measurable quantities.

cond-mat.str-el↗

arXiv2024

Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet

Competing interactions in quantum magnets lead to a variety of emergent states, including ordered phases, nematic magnets and quantum spin liquids. Among them, topological quantum magnets represent a promising platform to create topological excitations protected by the bulk many-body excitation gap. Here we establish the phase diagram of a breathing frustrated antiferromagnetic J1-J2-Heisenberg model, featuring both ordered states and a higher-order topological quantum magnet state. Using exact many-body methods based on neural network quantum states and tensor networks, we determine the existence of a first order phase transition between stripe order and the topological quantum magnet and the second order phase transition between the Neel order and quantum magnet phase, further corroborated by calculations of the many-body gap. Using an auxiliary fermion parton formalism, we show the emergence of topological spinon corner modes stemming from the breathing order parameter of the parent Heisenberg model. Our results establish the breathing frustrated square lattice Heisenberg model as a paradigmatic system to engineer topological quantum magnetism, as recently realized in Ti lattices at MgO.

cond-mat.str-el↗

arXiv2023

Lee-Yang theory of quantum phase transitions with neural network quantum states

Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.

cond-mat.str-el↗

arXiv2022

Lee-Yang theory of the two-dimensional quantum Ising model

Determining the phase diagram of interacting quantum many-body systems is an important task for a wide range of problems such as the understanding and design of quantum materials. For classical equilibrium systems, the Lee-Yang formalism provides a rigorous foundation of phase transitions, and these ideas have also been extended to the quantum realm. Here, we develop a Lee-Yang theory of quantum phase transitions that can include thermal fluctuations caused by a finite temperature, and it thereby provides a link between the classical Lee-Yang formalism and recent theories of phase transitions at zero temperature. Our methodology exploits analytic properties of the moment generating function of the order parameter in systems of finite size, and it can be implemented in combination with tensor-network calculations. Specifically, the onset of a symmetry-broken phase is signaled by the zeros of the moment generating function approaching the origin in the complex plane of a counting field that couples to the order parameter. Moreover, the zeros can be obtained by measuring or calculating the high cumulants of the order parameter. We determine the phase diagram of the two-dimensional quantum Ising model and thereby demonstrate the potential of our method to predict the critical behavior of two-dimensional quantum systems at finite temperatures.

cond-mat.stat-mech↗

arXiv2021

Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures

We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological invariants. In particular, we express the three-dimensional winding number of point-gapped non-Hermitian systems, which is defined as an integral over the whole Brillouin zone, in terms of symmetry eigenvalues at high-symmetry momenta. Furthermore, for time-reversal symmetric non-Hermitian topological insulators, we find that symmetry indicators characterize the associated Chern-Simons form, whose evaluation usually requires a computationally expensive choice of smooth gauge. In each case, we discuss the non-Hermitian surface states associated with nontrivial symmetry indicators.

cond-mat.mes-hall↗