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:cond-mat/0503354 · Journal of Physics A Mathematical and General

Supersymmetric model of spin-1/2 fermions on a chain

Raoul Santachiara, Kareljan Schoutens

Published Jun 1, 2005• 7 citations
arXivHTMLPDF

Abstract

In a recent work, N = 2 supersymmetry has been proposed as a tool for the analysis of itinerant, correlated fermions on a lattice. In this paper, we extend these considerations to the case of lattice fermions with spin 1/2. We introduce a model for correlated spin-1/2 fermions with a manifest N = 4 supersymmetry, and analyse its properties. The supersymmetric ground states that we find represent holes in an anti-ferromagnetic background.

DOI
10.1088/0305-4470/38/24/003

Related papers

Lattice fermion models with supersymmetry

Paul Fendley, Bernard Nienhuis, Kareljan Schoutens

We investigate a family of lattice models with manifest supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k = 1 model with the spin- antiferromagnetic XXZ chain at Δ = −1/2, and the k = 2 model with both the su (2|1)-symmetric tJ model in the ferromagnetic regime and the integrable spin-1 XXZ chain at . We argue that these models include critical points described by the superconformal minimal models.

arXiv:cond-mat/0307338•Journal of Physics A Mathematical and General•Dec 1, 2003•114 citations

Exact Ground State and Finite-Size Scaling in a Supersymmetric Lattice Model

Matteo Beccaria A, Gian Fabrizio De Angelis

We study a model of strongly correlated fermions in one dimension with extended N = 2 supersymmetry. The model is related to the spin S = 1/2 XXZ Heisenberg chain at anisotropy Delta = -1/2 with a real magnetic field on the boundary. We exploit the combinatorial properties of the ground state to determine its exact wave function on finite lattices with up to 30 sites. We compute several correlation functions of the fermionic and spin fields. We discuss the continuum limit by constructing lattice observables with well defined finite-size scaling behavior. For the fermionic model with periodic boundary conditions we give the emptiness formation probability in closed form.

arXiv:cond-mat/0407752•Physical Review Letters•Mar 14, 2005•33 citations

Spin Chains with Dynamical Lattice Supersymmetry

Christian Hagendorf

Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the $\\mathcal{N}=(2,2)$ superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension possess a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured

•Jan 1, 2013•35 citations

Lattice Models with N=2 Supersymmetry

Paul Fendley, Kareljan Schoutens, Jan De Boer A

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q+/- yield the Hamiltonian H=(Q(+),Q(-)) on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers; the Hamiltonian of our simplest model contains a hopping term and a repulsive potential. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless (1+1)-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.

arXiv:hep-th/0210161•Physical Review Letters•Mar 25, 2003•143 citations

Supersymmetry, lattice fermions, independence complexes and cohomology theory

Liza Huijse, Kareljan Schoutens

We analyze the quantum ground state structure of a specific model of itinerant, strongly interacting lattice fermions.The interactions are tuned to make the model supersymmetric.Due to this, quantum ground states are in one-to-one correspondence with cohomology classes of the so-called independence complex of the lattice.Our main result is a complete description of the cohomology, and thereby of the quantum ground states, for a two-dimensional square lattice with periodic boundary conditions.Our work builds on results by Jonsson, who determined the Euler characteristic (Witten index) via a correspondence with rhombus tilings of the plane.We prove a theorem, first conjectured by Fendley, which relates dimensions of the cohomology at grade n to the number of rhombus tilings with n rhombi.

arXiv:0903.0784•Advances in Theoretical and Mathematical Physics•Jan 1, 2010•44 citations

Supersymmetric models for fermions on a lattice

N. Ilieva, H. Narnhofer, W. Thirring

Abstract We investigate the large‐N behaviour of simple examples of supersymmetric interactions for fermions on a lattice. Witten's supersymmetric quantum mechanics and the BCS model appear just as two different aspects of one and the same model. For the BCS model, supersymmetry is only respected in a coherent superposition of Bogoliubov states. In this coherent superposition mesoscopic observables show better stability properties than in a Bogoliubov state.

arXiv:quant-ph/0502100•Fortschritte der Physik•Feb 3, 2006•7 citations
In a recent work, N = 2 supersymmetry has been proposed as a tool for the analysis of itinerant, correlated fermions on a lattice. In this paper, we extend these considerations to the case of lattice fermions with spin 1/2. We introduce a model for correlated spin-1/2 fermions with a manifest N = 4 supersymmetry, and analyse its properties. The supersymmetric ground states that we find represent holes in an anti-ferromagnetic background.
We investigate a family of lattice models with manifest supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k = 1 model with the spin- antiferromagnetic XXZ chain at Δ = −1/2, and the k = 2 model with both the su (2|1)-symmetric tJ model in the ferromagnetic regime and the integrable spin-1 XXZ chain at . We argue that these models include critical points described by the superconformal minimal models.
We study a model of strongly correlated fermions in one dimension with extended N = 2 supersymmetry. The model is related to the spin S = 1/2 XXZ Heisenberg chain at anisotropy Delta = -1/2 with a real magnetic field on the boundary. We exploit the combinatorial properties of the ground state to determine its exact wave function on finite lattices with up to 30 sites. We compute several correlation functions of the fermionic and spin fields. We discuss the continuum limit by constructing lattice observables with well defined finite-size scaling behavior. For the fermionic model with periodic boundary conditions we give the emptiness formation probability in closed form.
Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the mathcalN=(2,2)\\mathcal{N}=(2,2)mathcalN=(2,2) superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension possess a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured
We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q+/- yield the Hamiltonian H=(Q(+),Q(-)) on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers; the Hamiltonian of our simplest model contains a hopping term and a repulsive potential. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless (1+1)-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.
We analyze the quantum ground state structure of a specific model of itinerant, strongly interacting lattice fermions.The interactions are tuned to make the model supersymmetric.Due to this, quantum ground states are in one-to-one correspondence with cohomology classes of the so-called independence complex of the lattice.Our main result is a complete description of the cohomology, and thereby of the quantum ground states, for a two-dimensional square lattice with periodic boundary conditions.Our work builds on results by Jonsson, who determined the Euler characteristic (Witten index) via a correspondence with rhombus tilings of the plane.We prove a theorem, first conjectured by Fendley, which relates dimensions of the cohomology at grade n to the number of rhombus tilings with n rhombi.