Abstract
We studied a quantum spin chain invariant by the superalgebra osp(1|2). We derived non-linear integral equations for the row-to-row transfer matrix eigenvalue in order to analyze its finite size scaling behavior and we determined its central charge. We also studied the thermodynamical properties of the spin chain via non-linear integral equations for the quantum transfer matrix eigenvalue. We numerically solved these NLIE and evaluated the specific heat and magnetic susceptibility. The analytical low temperature analysis was performed providing the effective central charge. The computed values are in agreement with the numerical predictions in the literature.
Highlights
The notion of superalgebras[1] attracted a lot of attention and it was soon considered in the context of Yang-Baxter integrability
One can use the quantum transfer matrix approach to formulate different non-linear integral equations for the finite temperature case[16, 17, 18]
The negative central charge c = −2 obtained from the finite size analysis does not appear directly in the thermodynamical quantities, the different central charges obtained from finite size and finite temperature analysis are known to be related as follows[10]
Summary
The notion of superalgebras[1] attracted a lot of attention and it was soon considered in the context of Yang-Baxter integrability. The L-operator (3) satisfies the following properties: Regularity: L12(0) = a(0)P1g2, Thanks to these properties, we have that the logarithmic derivative of the rowto-row transfer matrix results in a quantum spin chain Hamiltonian, which can be written as, H. where J = 1, njσ = c†jσcjσ, Sjk = σσ′ Sσkσ′ c†jσcjσ′ (k = x, y, z) and cjσ are the “projected” fermionic operators acting on subspace |↑ , |0 , |↓ with grading {1, 0, 1}. In the coming sections we are going to derive NLIE for the largest eigenvalue of row-to-row/quantum transfer matrix for arbitrary finite size/temperature This will allow us to extract the information about the critical behaviour of the quantum spin chain as well as to provide accurate results for largest eigenvalue as a function of the system size and the thermodynamical properties as a function of temperature
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