On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

Hagendorf, Christian; Liénardy, Jean

doi:10.1088/1742-5468/aab01d

Cited by 7 publications

(21 citation statements)

References 35 publications

(135 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When λ 2 =−3 the bulk XXZ Hamiltonian conjugate to the DiSSEP ) † † q ĉ , q ĉ † are multiples of the spin reversed superchargeq, q † for H comb in equation (12), so substituting them into equation (7) gives 4H comb , consistently with equation (54).…”

Section: The Dissep At 3 2 L =And Lattice Susymentioning

confidence: 87%

Lattice SUSY for the DiSSEP at λ² = 1 (and λ² = −3)

Johnston

2019

J. Phys. Commun.

View full text Add to dashboard Cite

We investigate whether the dynamical lattice supersymmetry discussed for various Hamiltonians, including one-dimensional quantum spin chains, by (Fendley et al 2003 Hagendorf and Liénardy 2018 J. Stat. Mech. 033106) might also exist for the Markov matrices of any one-dimensional exclusion processes, which have the additional constraint of zero column sums by comparison with the spin chains. We find that the DiSSEP (Dissipative Symmetric Simple Exclusion Process), introduced by Crampe et al in (Crampe et al 2016 Phys. Rev. E 94, 032102; Vanicat [arXiv:1708.02440]), provides one such example for suitably chosen parameters. The DiSSEP Markov matrix admits the supersymmetry in these cases because it is conjugate to Ising (λ 2 = 1) and Δ = −1/ 2 XXZ (λ 2 = −3) spin chain Hamiltonians which also possess the supersymmetry. The consequences for the spectrum of the DiSSEP Markov matrix are discussed. We also note that the length-changing supersymmetry relation for the DiSSEP Markov matrix M L and the supercharge Q L † for L sites,, is reminiscent of a 'transfer matrix' symmetry that has been observed in other exclusion processes and discuss the similarity.

show abstract

Section: The Dissep At 3 2 L =And Lattice Susymentioning

confidence: 87%

Lattice SUSY for the DiSSEP at λ² = 1 (and λ² = −3)

Johnston

2019

J. Phys. Commun.

View full text Add to dashboard Cite

show abstract

“…We now construct a local supercharge that allows us to investigate the Hamiltonian (2). To this end, we define three local supercharges that satisfy (17). First, we introduce the operator q φ that acts on |ψ ∈ V according to q φ |ψ = |φ ⊗ |ψ + |ψ ⊗ |φ .…”

Section: The Supersymmetrymentioning

confidence: 99%

“…We evaluate this quotient by using the following proposition, whose proof is identical to the one of proposition 3.4 in [17].…”

Section: The Eigenvaluementioning

confidence: 99%

See 1 more Smart Citation

On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

Hagendorf

Liénardy

2020

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

The transfer matrix of the square-lattice eight-vertex model on a strip with L 1 vertical lines and open boundary conditions is investigated. It is shown that for vertex weights a, b, c, d that obey the relation (a 2 + ab)(b 2 + ab) = (c 2 + ab)(d 2 + ab) and appropriately chosen K-matrices K ± this transfer matrix possesses the remarkably simple, non-degenerate eigenvalue ΛL = (a + b) 2L tr(K + K − ). For positive vertex weights, ΛL is shown to be the largest transfer-matrix eigenvalue. The corresponding eigenspace is equal to the space of the ground states of the Hamiltonian of a related XYZ spin chain. An essential ingredient in the proofs is the supersymmetry of this Hamiltonian.

show abstract

“…Theorem 2 (Simple eigenvalue [16,19,20]) Let q = e 2πi/3 . The space of solutions of the eigenvalue problem T (z)|ψ = |ψ , M |ψ = µ|ψ (2.32)…”

Section: The Transfer Matrix Of the Six-vertex Modelmentioning

confidence: 99%

Boundary emptiness formation probabilities in the six-vertex model at $\mathbf{\Delta }=-\frac{\mathbf{1}}{\mathbf{2}}$

Morin-Duchesne¹,

Hagendorf²,

Cantini³

2020

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

We define a new family of overlaps C N,m for the XXZ Hamiltonian on a periodic chain of length N . These are equal to the linear sums of the groundstate components, in the canonical basis, wherein m consecutive spins are fixed to the state ↑. We define the boundary emptiness formation probabilities as the ratios C N,m /C N,0 of these overlaps. In the associated six-vertex model, they correspond to correlation functions on a semi-infinite cylinder of perimeter N . At the combinatorial point ∆ = − 1 2 , we obtain closed-form expressions in terms of simple products of ratios of integers.

show abstract

On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

Cited by 7 publications

References 35 publications

Lattice SUSY for the DiSSEP at λ² = 1 (and λ² = −3)

Lattice SUSY for the DiSSEP at λ² = 1 (and λ² = −3)

On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

Boundary emptiness formation probabilities in the six-vertex model at $\mathbf{\Delta }=-\frac{\mathbf{1}}{\mathbf{2}}$

Contact Info

Product

Resources

About

On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions

Cited by 7 publications

References 35 publications

Lattice SUSY for the DiSSEP at λ2 = 1 (and λ2 = −3)

Lattice SUSY for the DiSSEP at λ2 = 1 (and λ2 = −3)

On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions

Boundary emptiness formation probabilities in the six-vertex model at $\mathbf{\Delta }=-\frac{\mathbf{1}}{\mathbf{2}}$

Contact Info

Product

Resources

About

Lattice SUSY for the DiSSEP at λ² = 1 (and λ² = −3)

Lattice SUSY for the DiSSEP at λ² = 1 (and λ² = −3)