# Exact and simple results for the XYZ and strongly interacting fermion chains

@article{Fendley2010ExactAS, title={Exact and simple results for the XYZ and strongly interacting fermion chains}, author={Paul Fendley and Christian Hagendorf}, journal={Journal of Physics A}, year={2010}, volume={43}, pages={402004} }

We conjecture exact and simple formulas for some physical quantities in two quantum chains. A classic result of this type is Onsager, Kaufman and Yang's formula for the spontaneous magnetization in the Ising model, subsequently generalized to the chiral Potts models. We conjecture that analogous results occur in the XYZ chain when the couplings obey JxJy + JyJz + JxJz = 0, and in a related fermion chain with strong interactions and supersymmetry. We find exact formulas for the magnetization and…

## 20 Citations

Ground-state properties of a supersymmetric fermion chain

- Physics, Mathematics
- 2011

We analyze the ground state of a strongly interacting fermion chain with a supersymmetry. We conjecture a number of exact results, such as a hidden duality between weak and strong couplings. By…

The Eight-Vertex Model and Lattice Supersymmetry

- Physics, Mathematics
- 2011

We show that the XYZ spin chain along the special line of couplings JxJy+JxJz+JyJz=0 possesses a hidden $\mathcal{N}=(2,2)$ supersymmetry. This lattice supersymmetry is non-local and changes the…

A staggered fermion chain with supersymmetry on open intervals

- Physics
- 2012

A strongly interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the…

Lattice supersymmetry in the open XXZ model: An algebraic Bethe Ansatz analysis

- Physics, Mathematics
- 2017

We reconsider the open XXZ chain of Yang and Fendley. This model possesses a lattice supersymmetry which changes the length of the chain by one site. We perform an algebraic Bethe ansatz analysis of…

Spin Chains with Dynamical Lattice Supersymmetry

- Physics, Mathematics
- 2013

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…

Bethe ansatz solvability and supersymmetry of the M2 model of single fermions and pairs

- Physics, Mathematics
- 2014

A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice N = 2 supersymmetry is presented. A submanifold in the space of parameters of the model where it is…

Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D

- Mathematics, Physics
- 2011

We present a full identification of lattice model properties with their field theoretical counterparts in the continuum limit for a supersymmetric model for itinerant spinless fermions on a…

M$_k$ models: the field theory connection

- Physics
- 2017

The Mk models for 1D lattice fermions are characterised by N=2 supersymmetry and by an order-k clustering property. This paper highlights connections with quantum field theories (QFTs) in various…

Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality

- Physics, Mathematics
- 2012

We study a model for itinerant, strongly interacting fermions where a judicious tuning of the interactions leads to a supersymmetric Hamiltonian. On the triangular lattice this model is known to…

Supersymmetric lattice models: Field theory correspondence, integrability, defects and degeneracies

- Physics
- 2016

In this PhD thesis lattice models of interacting spinless fermions with an explicit supersymmetry are studied in one-dimension. The interactions between the particles in these models occur because of…

## References

SHOWING 1-10 OF 56 REFERENCES

Exact ground state and finite-size scaling in a supersymmetric lattice model.

- Physics, MedicinePhysical review letters
- 2005

The continuum limit is discussed by constructing lattice observables with well defined finite-size scaling behavior by exploiting the combinatorial properties of the ground state to determine its exact wave function on finite lattices with up to 30 sites.

Lattice fermion models with supersymmetry

- Physics
- 2003

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…

Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant DPQ

- Mathematics, Physics
- 2010

For the Ising model, the calculation of the spontaneous magnetization leads to the problem of evaluating a determinant. Yang did this by calculating the eigenvalues in the large-lattice limit.…

Non-local spacetime supersymmetry on the lattice

- Mathematics, Physics
- 2004

We show that several well-known one-dimensional quantum systems possess a hidden non-local supersymmetry. The simplest example is the open XXZ spin chain with Δ = −1/2. We use the supersymmetry to…

Critical Exponents of the Chiral Potts Model from Conformal Field Theory

- Physics
- 1993

Abstract The Z N - invariant chiral Potts model is considered as a perturbation of Z N conformal field theory. In the self-dual case the renormalization group equations become simple, and yield…

Excitation spectrum and order parameter for the integrable N-state chiral potts model

- Physics
- 1989

The integrable N-state chiral Potts model is the first solvable model where Boltzmann weights lie on c curve of genus greater than one. We here study the eigenvalues and order parameter. For the…

QUANTUM MODEL FOR COMMENSURATE - INCOMMENSURATE TRANSITIONS

- Physics
- 1983

A one-dimensional quantum mechanical model with three states per site is considered. Its ground state shows several commensurate-incommensurate transitions analogous to ones previously studied in…

Lattice models with N=2 supersymmetry.

- Physics, MedicinePhysical review letters
- 2003

This work introduces lattice models with explicit N=2 supersymmetry, and analyzes these models using conformal field theory, the Bethe ansatz, and cohomology.

A possible combinatorial point for the XYZ spin chain

- Mathematics, Physics
- 2010

We formulate and discuss several conjectures related to the ground state vectors of odd-length XYZ spin chains with periodic boundary conditions and a special choice of the Hamiltonian parameters. In…

Scattering and thermodynamics of fractionally-charged supersymmetric solitons

- Physics
- 1991

Abstract We show that there are solitons with fractional fermion number in integrable N = 2 supersymmetric models. We obtain the soliton S -matrix for the minimal, N = 2 supersymmetric theory…