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/0410749 · Journal of Physics A Mathematical and General

New conjecture for the SUq(N) Perk–Schultz models

F C Alcaraz, Yu G Stroganov

Published Nov 18, 2004• 0 citations
arXivHTMLPDF

Abstract

We present a new conjecture for the SU q ( N ) Perk–Schultz models. This conjecture extends a conjecture presented in our article ( Alcaraz F C and Stroganov Yu G J. Phys. A: Math. Gen. 35 6767–87 ).
DOI
10.1088/0305-4470/37/48/013

Related papers

Nonlinear integral equations and high temperature expansion for the Uq(slˆ(r+1|s+1)) Perk–Schultz model

Zengo Tsuboi

arXiv:cond-mat/0510458•Nuclear Physics B•Jan 19, 2006•21 citations

Nested Bethe ansatz for Perk–Schultz model with open boundary conditions

Guang-Liang Li, Rui‐Hong Yue, Bo-Yu Hou

Nuclear Physics B•Oct 1, 2000•24 citations

New conjecture for the SUq(N) Perk-Schultz models

Francisco Castilho Alcaraz, Yu. G. Stroganov

In [1] (to which we refer to hereafter by I), based on numerical evidence, we present a series of conjectures about the eigenspectra of the SUq(N) invariant Perk-Schultz Hamiltonians, given by I.1 with p = 0. Subsequent extensive numerical work indicate that the conjecture (3) of I (I.85) is just a particular case of a more general one, relating the ground-state energy of diferent SUq(N) quantum chains. This new conjecture can be stated as follows: Conjecture: The difference of the ground-state energy of the SUq(N) and SUq ′(K) model in an open chain of lenght L is given by E0[SUq(N), q = e iπK/(N+K) ] − E0[SUq(N), q = e iπN/(N+K) ] = π(N − K) 2(1 − L) sin (), (1) 2(N + K) where N = K = 1, 2,... and E0[SUq(1), q)] = 0. The particular case N> 1 and K = 1 gives E0[SUq(N), q = e iπ/(N+1) π(N − 1)] = 2(1 − L) sin (), (2) 2(N + 1) recovering the earlier announced conjecture (I.85). The results (1) and (2) give exact finite-size corrections suporting earlier conjectures about the op-1 erator content of the Perk-Schultz models. As is well known [2] as a consequence of conformal invariance the finite-size corrections of the ground-state energy of critical chains with free boundary conditions are given by E0(L)/L = e ∞ + f∞/L − πc 24L 2 + o(L−2), (3) where e ∞ (f∞) is the ground-state energy per site (surface energy) at the bulk limit L → ∞, and c is the conformal anomaly of the effective underlying conformal field theory defined on a semi-infinte plane. The relations (3) and (2) imply that in the case of the SUq(N) model with q = exp(iπN/(N + 1)) the conformal anomaly has the value c = 0 for all N ≥ 2 and π(N − 1) e ∞ = −f ∞ = −2 sin (. (4) 2(N + 1) Moreover all the other finite-size corrections appearing in (3) are identically zero! This result can be understood from the conjectured operator content of the model. The conformal dimensions of the SUq(N) model are expected to be given by a generalized coulomb gas description x(n, m) = xp

•Jan 1, 2004•0 citations

A novel coproduct of suq(2) and its relation to XXZ spin chain model

L. C. Kwek, C. H. Oh, Kuldip Singh

Physics Letters A•Feb 1, 2001•0 citations

Generalization of the matrix product ansatz for integrable chains

Francisco Castilho Alcaraz, Matheus J. Lazo

We present a general formulation of the matrix product ansatz for exactly integrable chains on periodic lattices. This new formulation extends the matrix product ansatz present in our previous articles ( F C Alcaraz and M J Lazo 2004 J. Phys. A: Math. Gen. 37 L1–L7 and F C Alcaraz and M J Lazo 2004 J. Phys. A: Math. Gen. 37 4149–82 ).

arXiv:cond-mat/0608177•Journal of Physics A Mathematical and General•Aug 18, 2006•32 citations

Spin chains and combinatorics

A. V. Razumov, Yu. G. Stroganov

In this paper we continue the investigation of finite XXZ spin chains with periodic boundary conditions and odd number of sites, initiated in our previous article (Stroganov Yu G 2001 J. Phys. A: Math. Gen. 34 L179-85 ). As it turned out, for a special value of the asymmetry parameter Δ = -1/2 the Hamiltonian of the system has an eigenvalue, which is exactly proportional to the number of sites E = -3 N /2. Using Mathematica we have found explicitly the corresponding eigenvectors for N ⩽17. The obtained results support the conjecture our paper that this special eigenvalue corresponds to the ground state vector. We make a lot of conjectures concerning the correlations of the model. Many remarkable relations between the wavefunction components are noted. It turns out, for example, that the ratio of the largest component to the least one is equal to the number of the alternating sign matrices.

arXiv:cond-mat/0012141•Journal of Physics A Mathematical and General•Mar 30, 2001•217 citations
In [1] (to which we refer to hereafter by I), based on numerical evidence, we present a series of conjectures about the eigenspectra of the SUq(N) invariant Perk-Schultz Hamiltonians, given by I.1 with p = 0. Subsequent extensive numerical work indicate that the conjecture (3) of I (I.85) is just a particular case of a more general one, relating the ground-state energy of diferent SUq(N) quantum chains. This new conjecture can be stated as follows: Conjecture: The difference of the ground-state energy of the SUq(N) and SUq ′(K) model in an open chain of lenght L is given by E0[SUq(N), q = e iπK/(N+K) ] − E0[SUq(N), q = e iπN/(N+K) ] = π(N − K) 2(1 − L) sin (), (1) 2(N + K) where N = K = 1, 2,... and E0[SUq(1), q)] = 0. The particular case N> 1 and K = 1 gives E0[SUq(N), q = e iπ/(N+1) π(N − 1)] = 2(1 − L) sin (), (2) 2(N + 1) recovering the earlier announced conjecture (I.85). The results (1) and (2) give exact finite-size corrections suporting earlier conjectures about the op-1 erator content of the Perk-Schultz models. As is well known [2] as a consequence of conformal invariance the finite-size corrections of the ground-state energy of critical chains with free boundary conditions are given by E0(L)/L = e ∞ + f∞/L − πc 24L 2 + o(L−2), (3) where e ∞ (f∞) is the ground-state energy per site (surface energy) at the bulk limit L → ∞, and c is the conformal anomaly of the effective underlying conformal field theory defined on a semi-infinte plane. The relations (3) and (2) imply that in the case of the SUq(N) model with q = exp(iπN/(N + 1)) the conformal anomaly has the value c = 0 for all N ≥ 2 and π(N − 1) e ∞ = −f ∞ = −2 sin (. (4) 2(N + 1) Moreover all the other finite-size corrections appearing in (3) are identically zero! This result can be understood from the conjectured operator content of the model. The conformal dimensions of the SUq(N) model are expected to be given by a generalized coulomb gas description x(n, m) = xp
In this paper we continue the investigation of finite XXZ spin chains with periodic boundary conditions and odd number of sites, initiated in our previous article (Stroganov Yu G 2001 J. Phys. A: Math. Gen. 34 L179-85 ). As it turned out, for a special value of the asymmetry parameter Δ = -1/2 the Hamiltonian of the system has an eigenvalue, which is exactly proportional to the number of sites E = -3 N /2. Using Mathematica we have found explicitly the corresponding eigenvectors for N ⩽17. The obtained results support the conjecture our paper that this special eigenvalue corresponds to the ground state vector. We make a lot of conjectures concerning the correlations of the model. Many remarkable relations between the wavefunction components are noted. It turns out, for example, that the ratio of the largest component to the least one is equal to the number of the alternating sign matrices.