Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1806.06542 · Physical review. B./Physical review. B

Frustrated quantum spin systems in small triangular lattices studied with a numerical method

David Castells-Graells, A. Yuste, Anna Sanpera

Published Oct 10, 2019• 4 citations
arXivHTMLPDF

Abstract

The study of quantum frustrated systems remains one of the most challenging subjects of quantum magnetism, as they can hold quantum spin liquids, whose characterization is quite elusive. The presence of gapped quantum spin liquids possessing long-range entanglement while being locally indistinguishable often demands highly sophisticated numerical approaches for their description. Here we propose an easy computational method based on exact diagonalization with engineered boundary conditions in very small plaquettes. We apply the method to study the quantum phase diagram of diverse antiferromagnetic frustrated Heisenberg models in the triangular lattice. Our results are in qualitative agreement with previous results obtained by means of sophisticated methods like density matrix renormalization group (2D-DMRG) or variational quantum Monte Carlo.

DOI
10.1103/physrevb.100.155119

Related papers

Using random boundary conditions to simulate disordered quantum spin models in two-dimensional systems

A. Yuste, Maria Moreno-Cardoner, Anna Sanpera

Disordered quantum antiferromagnets in two-dimensional compounds have been a focus of interest in the last years due to their exotic properties. However, with very few exceptions, the ground states of the corresponding Hamiltonians are notoriously difficult to simulate making their characterization and detection very elusive, both theoretically and experimentally. Here we propose a method to signal quantum disordered antiferromagnets by doing exact diagonalization in small lattices using random boundary conditions and averaging the observables of interest over the different disorder realizations. We apply our method to study the Heisenberg spin-1/2 model in an anisotropic triangular lattice. In this model, the competition between frustration and quantum fluctuations might lead to some spin-liquid phases as predicted from different methods ranging from spin-wave mean-field theory to 2D-DMRG or PEPS. Our method accurately reproduces the ordered phases expected of the model and signals quantum disordered phases by the presence of a large number of quasidegenerate ground states together with an undefined local order parameter. The method presents a weak dependence on finite-size effects.

arXiv:1612.00381•Physical review. B./Physical review. B•May 30, 2017•4 citations

Topological States of Matter in Frustrated Quantum Magnetism

Alexander Wietek

Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin models. We develop novel algorithms for large-scale Exact Diagonalization computations. Sublattice coding methods for efficient use of lattice symmetries in the procedure of diagonalizing the Hamiltonian matrix are proposed and suggest a randomized distributed memory parallelization strategy. Benchmarks of computations on various supercomputers with system size up to 50 spin-1/2 particles have been performed. Results concerning the emergence of a chiral spin liquid in a frustrated kagome Heisenberg antiferromagnet are presented. The stability and extent of this phase are discussed. In an extended Heisenberg model on the triangular lattice, we establish another chiral spin liquid phase. We discuss the special case of the Heisenberg $J_1$-$J_2$ model and present a scenario where the critical point of phase transition from the 120-degree Néel to a putative $\mathbf{Z}_2$ spin liquid is described by a Dirac spin liquid. A generalization of the SU(2) Heisenberg model with SU(N) degrees of freedom on the triangular lattice with an additional ring-exchange term is discussed. We present our contribution to the project and the final results that suggest a series of chiral spin liquid phases in an extended parameter range. Finally, we present preliminary data from a Quantum Monte Carlo study of an SU(N) version of the J-Q model on a square lattice for N=2,...,10, and multi-column representations. We establish the phase boundary between the Néel ordered phase and the disordered phases. The disordered phase in the four-column representation is expected to be a two-dimensional analog of the Haldane phase for the spin-1 Heisenberg chain.

arXiv:2210.03511•Oct 7, 2022•1 citation

Investigation of Frustrated Quantum Spin Systems Using Tensor Network and Machine Learning Approaches

Vít Anderle

In this thesis, we investigate frustrated systems with focus on the triangular lattice anisotropic Heisenberg antiferromagnet. Firstly, we examined the material CeMgAl11O19 as a potential quantum spin liquid utilizing the density matrix renormalization group method (DMRG). Two different low-temperature effective models have been proposed. The first was motivated by similar systems and contains long-range exchange interac- tion. The second, introduced much later, assumes only nearest-neighbor interactions and exhibits strong anisotropy, mixing ferromagnetic and antiferromagnetic couplings. We showed that the first model does not reproduce the experimental results even qual- itatively, but the second is consistent with the measured data. Our analysis demon- strated that CeMgAl11O19 is farther away from the critical point than previously claimed in the literature. We then investigated the second model in more detail and examined its complicated ground state phase diagram in magnetic field. The complicated struc- ture of the diagram was analyzed by unsupervised machine learning techniques as well as by employing order parameters constructed from structure factors. Finally, we used the recently introduced variational Monte Carlo based on neural network quantum states (NNQS) to investigate the ground state of...

•Jan 1, 2025•0 citations

Nature of quantum spin liquids of the S = 1 2 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study

Yi‐Fan Jiang, Hong‐Chen Jiang

We study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-$1/2$ antiferromagnetic Heisenberg model on the triangular lattice with nearest- $({J}_{1})$, next-nearest- $({J}_{2})$, and third-neighbor $({J}_{3})$ interactions by using the density-matrix renormalization group (DMRG) method. By combining parallel DMRG with $\mathrm{SU}(2)$ spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to ${L}_{x}=48$ and circumference ${L}_{y}=6--12$. Our results suggest that the QSL phase of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model is gapped, which is characterized by the absence of a gapless mode and by short-range spin-spin and dimer-dimer correlations. In the presence of ${J}_{3}$ interaction, we find that a critical QSL with a single gapless mode emerges. While both spin-spin and scalar chiral-chiral correlations are short ranged, dimer-dimer correlations are quasi long ranged and decay as a power law at long distances.

arXiv:2203.10216•Physical review. B./Physical review. B•Apr 27, 2023•20 citations

Quantum phase diagrams and phase transitions in frustrated two-dimensional Heisenberg models

D. N. Sheng

The quantum spin liquid is an emergent state of matter, which has attracted a lot of recent attention. I will review recent numerical progress based on the density matrix renormalization calculations in identifying gapped spin liquid in twodimensional frustrated spin systems. I will first focus on extended model with Heisenberg exchange couplings on kagome lattice and demonstrate a topological state with fractionalized spinon and emergent gauge field clearly shown in numerical simulations. I will present concrete results on the quantum phase diagram of the extended kagome Heisenberg model, and compare that with the phase diagrams of the square and honeycomb lattice models with the dominant plaquette valence bond phase in nonmagnetic region. I will discuss numerical effort and theoretical challenge in fully pinning down the nature of the gapped topological phase, and also the nature of the quantum phase transitions in these Heisenberg systems.

Bulletin of the American Physical Society•Mar 3, 2014•0 citations

Triangular J 1 − J 2 Heisenberg antiferromagnet in a magnetic field

Thomas Bader, Shi Feng, Sasank Budaraju +3 more

The behavior of the paradigmatic J 1 − J 2 triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaus across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around J 2 / J 1 = 1 8 in which (i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and (ii) by further increasing the field, two plateaus are clearly obtained at m = 1 3 and m = 1 2 . We discuss the experimental importance of the consecutive magnetization plateau transitions as a signature of an underlying quantum spin-liquid phase.

arXiv:2512.08768•Physical review. B./Physical review. B•May 22, 2026•3 citations
The study of quantum frustrated systems remains one of the most challenging subjects of quantum magnetism, as they can hold quantum spin liquids, whose characterization is quite elusive. The presence of gapped quantum spin liquids possessing long-range entanglement while being locally indistinguishable often demands highly sophisticated numerical approaches for their description. Here we propose an easy computational method based on exact diagonalization with engineered boundary conditions in very small plaquettes. We apply the method to study the quantum phase diagram of diverse antiferromagnetic frustrated Heisenberg models in the triangular lattice. Our results are in qualitative agreement with previous results obtained by means of sophisticated methods like density matrix renormalization group (2D-DMRG) or variational quantum Monte Carlo.
Disordered quantum antiferromagnets in two-dimensional compounds have been a focus of interest in the last years due to their exotic properties. However, with very few exceptions, the ground states of the corresponding Hamiltonians are notoriously difficult to simulate making their characterization and detection very elusive, both theoretically and experimentally. Here we propose a method to signal quantum disordered antiferromagnets by doing exact diagonalization in small lattices using random boundary conditions and averaging the observables of interest over the different disorder realizations. We apply our method to study the Heisenberg spin-1/2 model in an anisotropic triangular lattice. In this model, the competition between frustration and quantum fluctuations might lead to some spin-liquid phases as predicted from different methods ranging from spin-wave mean-field theory to 2D-DMRG or PEPS. Our method accurately reproduces the ordered phases expected of the model and signals quantum disordered phases by the presence of a large number of quasidegenerate ground states together with an undefined local order parameter. The method presents a weak dependence on finite-size effects.
Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin models. We develop novel algorithms for large-scale Exact Diagonalization computations. Sublattice coding methods for efficient use of lattice symmetries in the procedure of diagonalizing the Hamiltonian matrix are proposed and suggest a randomized distributed memory parallelization strategy. Benchmarks of computations on various supercomputers with system size up to 50 spin-1/2 particles have been performed. Results concerning the emergence of a chiral spin liquid in a frustrated kagome Heisenberg antiferromagnet are presented. The stability and extent of this phase are discussed. In an extended Heisenberg model on the triangular lattice, we establish another chiral spin liquid phase. We discuss the special case of the Heisenberg J1J_1J1​-J2J_2J2​ model and present a scenario where the critical point of phase transition from the 120-degree Néel to a putative Z2\mathbf{Z}_2Z2​ spin liquid is described by a Dirac spin liquid. A generalization of the SU(2) Heisenberg model with SU(N) degrees of freedom on the triangular lattice with an additional ring-exchange term is discussed. We present our contribution to the project and the final results that suggest a series of chiral spin liquid phases in an extended parameter range. Finally, we present preliminary data from a Quantum Monte Carlo study of an SU(N) version of the J-Q model on a square lattice for N=2,...,10, and multi-column representations. We establish the phase boundary between the Néel ordered phase and the disordered phases. The disordered phase in the four-column representation is expected to be a two-dimensional analog of the Haldane phase for the spin-1 Heisenberg chain.
In this thesis, we investigate frustrated systems with focus on the triangular lattice anisotropic Heisenberg antiferromagnet. Firstly, we examined the material CeMgAl11O19 as a potential quantum spin liquid utilizing the density matrix renormalization group method (DMRG). Two different low-temperature effective models have been proposed. The first was motivated by similar systems and contains long-range exchange interac- tion. The second, introduced much later, assumes only nearest-neighbor interactions and exhibits strong anisotropy, mixing ferromagnetic and antiferromagnetic couplings. We showed that the first model does not reproduce the experimental results even qual- itatively, but the second is consistent with the measured data. Our analysis demon- strated that CeMgAl11O19 is farther away from the critical point than previously claimed in the literature. We then investigated the second model in more detail and examined its complicated ground state phase diagram in magnetic field. The complicated struc- ture of the diagram was analyzed by unsupervised machine learning techniques as well as by employing order parameters constructed from structure factors. Finally, we used the recently introduced variational Monte Carlo based on neural network quantum states (NNQS) to investigate the ground state of...
We study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-1/21/21/2 antiferromagnetic Heisenberg model on the triangular lattice with nearest- (J1)({J}_{1})(J1​), next-nearest- (J2)({J}_{2})(J2​), and third-neighbor (J3)({J}_{3})(J3​) interactions by using the density-matrix renormalization group (DMRG) method. By combining parallel DMRG with SU(2)\mathrm{SU}(2)SU(2) spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to Lx=48{L}_{x}=48Lx​=48 and circumference Ly=6−−12{L}_{y}=6--12Ly​=6−−12. Our results suggest that the QSL phase of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model is gapped, which is characterized by the absence of a gapless mode and by short-range spin-spin and dimer-dimer correlations. In the presence of J3{J}_{3}J3​ interaction, we find that a critical QSL with a single gapless mode emerges. While both spin-spin and scalar chiral-chiral correlations are short ranged, dimer-dimer correlations are quasi long ranged and decay as a power law at long distances.
The quantum spin liquid is an emergent state of matter, which has attracted a lot of recent attention. I will review recent numerical progress based on the density matrix renormalization calculations in identifying gapped spin liquid in twodimensional frustrated spin systems. I will first focus on extended model with Heisenberg exchange couplings on kagome lattice and demonstrate a topological state with fractionalized spinon and emergent gauge field clearly shown in numerical simulations. I will present concrete results on the quantum phase diagram of the extended kagome Heisenberg model, and compare that with the phase diagrams of the square and honeycomb lattice models with the dominant plaquette valence bond phase in nonmagnetic region. I will discuss numerical effort and theoretical challenge in fully pinning down the nature of the gapped topological phase, and also the nature of the quantum phase transitions in these Heisenberg systems.
The behavior of the paradigmatic J 1 − J 2 triangular lattice Heisenberg antiferromagnet in a magnetic field remains unsettled despite decades of study. We map out the phase diagram using three complementary approaches, including self-consistent nonlinear spin-wave theory, density-matrix renormalization group, and variational Monte Carlo. This combined analysis resolves the competition among different field-induced magnetic orders and magnetization plateaus across the classically frustrated parameter range. In particular, there is a finite range in the parameter regime around J 2 / J 1 = 1 8 in which (i) upon the application of the external field, the gapless quantum spin liquid acquires a finite density of monopoles, and (ii) by further increasing the field, two plateaus are clearly obtained at m = 1 3 and m = 1 2 . We discuss the experimental importance of the consecutive magnetization plateau transitions as a signature of an underlying quantum spin-liquid phase.