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

International Journal of Modern Physics B

NUMERICAL STUDIES OF STRONGLY CORRELATED ELECTRONIC MODELS

Elbio R. Dagotto

Published Jan 1, 1991• 40 citations
Publisher

Abstract

Recent numerical work on strongly correlated electronic models using the Lanczos approach is reviewed. In particular static and dynamical properties of the Hubbard, t—J (with one, two and more holes) and the spin-½ Heisenberg antiferromagnet are presented. An attempt to summarize the current active search for nontrivial ground states of the frustrated Heisenberg model is made. Numerical methods like the Lanczos technique are providing useful information in the study of these models.

DOI
10.1142/s0217979291000067

Related papers

THE t-J AND FRUSTRATED HEISENBERG MODELS: A STATUS REPORT ON NUMERICAL STUDIES

Elbio R. Dagotto

Recent numerical work on the t-J model and the frustrated spin-[Formula: see text] Heisenberg antiferromagnet is reviewed. Lanczos results are mainly discussed but other methods are also mentioned. Static and dynamical properties of one and more holes in the t-J model are presented. The current active search for nontrivial ground states of the frustrated Heisenberg model is summarized. It is concluded that numerical methods are providing useful information in the study of these models.

International Journal of Modern Physics B•Apr 1, 1991•60 citations

High Tc superconductors: Numerical studies of the Hubbard model

Elbio R. Dagotto

Recent numerical work on strongly correlated electronic models using the Lanczos approach is reviewed. In particular, static and dynamical properties of the Hubbard and t–J models are presented attempting to make a connection with experiments. We conclude that numerical methods like the Lanczos technique are providing useful information in the study of these models.

AIP conference proceedings•Jan 1, 1992•1 citation

Correlation functions of the antiferromagnetic Heisenberg model using a modified Lanczos method

Eduardo R. Gagliano, Elbio R. Dagotto, Adriana Moreo +1 more

Using a modified Lanczos algorithm, we study the correlation functions in the ground state of the one-dimensional antiferromagnetic Heisenberg model. We obtain numerical results for rings up to 24 sites. There are no indications of the anomalous behavior of these correlation functions recently observed in chains with 16 sites. We also present a pedagogical description of the hashing technique which is an efficient algorithm for searching and storage purposes.

Physical review. B, Condensed matter•Aug 1, 1986•213 citations

NUMERICAL SIMULATIONS OF STRONGLY CORRELATED ELECTRON AND SPIN SYSTEMS

Hitesh J. Changlani

Developing analytical and numerical tools for strongly correlated systems is a central challenge for the condensed matter physics community. In the absence of exact solutions and controlled analytical approximations, numerical techniques have often contributed to our understanding of these systems. Exact Diagonalization (ED) requires the storage of at least two vectors the size of the Hilbert space under consideration (which grows exponentially with system size) which makes it affordable only for small systems. The Density Matrix Renormalization Group (DMRG) uses an intelligent Hilbert space truncation procedure to significantly reduce this cost, but in its present formulation is limited to quasi-1D systems. Quantum Monte Carlo (QMC) maps the Schrödinger equation to the diffusion equation (in imaginary time) and only samples the eigenvector over time, thereby avoiding the memory limitation. However, the stochasticity involved in the method gives rise to the the "sign problem" characteristic of fermion and frustrated spin systems. The first part of this thesis is an effort to make progress in the development of a numerical technique which overcomes the above mentioned problems. We consider novel variational wavefunctions, christened "Correlator Product States" (CPS), that have a general functional form which hopes to capture essential correlations in the ground states of spin and fermion systems in any dimension. We also consider a recent proposal to modify projector (Green's Function) Quantum Monte Carlo to ameliorate the sign problem for realistic and model Hamiltonians (such as the Hubbard model). This exploration led to our own set of improvements, primarily a semistochastic formulation of projector Quantum Monte Carlo. Despite their limitations, existing numerical techniques can yield physical insights into a wide variety of problems. The second part of this thesis considers one such numerical technique - DMRG - and adapts it to study the Heisenberg antiferromagnet on a generic tree graph. Our attention turns to a systematic numerical and semi-analytical study of the effect of local even/odd sublattice imbalance on the low energy spectrum of antiferromagnets on regular Cayley trees. Finally, motivated by previous experiments and theories of randomly diluted antiferromagnets (where an even/odd sublattice imbalance naturally occurs), we present our study of the Heisenberg antiferromagnet on the Cayley tree at the percolation threshold. Our work shows how to detect "emergent" low energy degrees of freedom and compute the effective interactions between them by using data from DMRG calculations.

•Jan 28, 2013•0 citations

Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons

Derzhko, O., Johannes Richter, Maksymenko, M.

nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system.As a result, the ground-state and lowtemperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems.In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field.Main emphasis is made on recent developments which include results for both spin and electron flat-band models.In particular, for flat-band spin systems we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry.For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems.Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

•May 10, 2015•199 citations

NUMERICAL STUDY OF THE t−J MODEL: EXACT GROUND STATE AND FLUX PHASES

Yukio Hasegawa, Didier Poilblanc

Strongly correlated 2D electrons described by the t–J model are investigated numerically. Exact ground state for one and two holes in a finite cluster with periodic boundary conditions are obtained by using the Lanczos algorithm. The effects of Coulomb repulsion of the holes on the nearest neighbor sites are taken into account. Commensurate flux phases are investigated for the same size of clusters. They are shown to be a good approximation for the ground state specially in the intermediate value of J/t.

International Journal of Modern Physics B•Dec 1, 1989•3 citations
Recent numerical work on strongly correlated electronic models using the Lanczos approach is reviewed. In particular static and dynamical properties of the Hubbard, t—J (with one, two and more holes) and the spin-½ Heisenberg antiferromagnet are presented. An attempt to summarize the current active search for nontrivial ground states of the frustrated Heisenberg model is made. Numerical methods like the Lanczos technique are providing useful information in the study of these models.
Developing analytical and numerical tools for strongly correlated systems is a central challenge for the condensed matter physics community. In the absence of exact solutions and controlled analytical approximations, numerical techniques have often contributed to our understanding of these systems. Exact Diagonalization (ED) requires the storage of at least two vectors the size of the Hilbert space under consideration (which grows exponentially with system size) which makes it affordable only for small systems. The Density Matrix Renormalization Group (DMRG) uses an intelligent Hilbert space truncation procedure to significantly reduce this cost, but in its present formulation is limited to quasi-1D systems. Quantum Monte Carlo (QMC) maps the Schrödinger equation to the diffusion equation (in imaginary time) and only samples the eigenvector over time, thereby avoiding the memory limitation. However, the stochasticity involved in the method gives rise to the the "sign problem" characteristic of fermion and frustrated spin systems. The first part of this thesis is an effort to make progress in the development of a numerical technique which overcomes the above mentioned problems. We consider novel variational wavefunctions, christened "Correlator Product States" (CPS), that have a general functional form which hopes to capture essential correlations in the ground states of spin and fermion systems in any dimension. We also consider a recent proposal to modify projector (Green's Function) Quantum Monte Carlo to ameliorate the sign problem for realistic and model Hamiltonians (such as the Hubbard model). This exploration led to our own set of improvements, primarily a semistochastic formulation of projector Quantum Monte Carlo. Despite their limitations, existing numerical techniques can yield physical insights into a wide variety of problems. The second part of this thesis considers one such numerical technique - DMRG - and adapts it to study the Heisenberg antiferromagnet on a generic tree graph. Our attention turns to a systematic numerical and semi-analytical study of the effect of local even/odd sublattice imbalance on the low energy spectrum of antiferromagnets on regular Cayley trees. Finally, motivated by previous experiments and theories of randomly diluted antiferromagnets (where an even/odd sublattice imbalance naturally occurs), we present our study of the Heisenberg antiferromagnet on the Cayley tree at the percolation threshold. Our work shows how to detect "emergent" low energy degrees of freedom and compute the effective interactions between them by using data from DMRG calculations.
nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system.As a result, the ground-state and lowtemperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems.In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field.Main emphasis is made on recent developments which include results for both spin and electron flat-band models.In particular, for flat-band spin systems we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry.For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems.Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.
Strongly correlated 2D electrons described by the t–J model are investigated numerically. Exact ground state for one and two holes in a finite cluster with periodic boundary conditions are obtained by using the Lanczos algorithm. The effects of Coulomb repulsion of the holes on the nearest neighbor sites are taken into account. Commensurate flux phases are investigated for the same size of clusters. They are shown to be a good approximation for the ground state specially in the intermediate value of J/t.