arXiv subjects

Bireswar Basu-Mallick

Publications and source records attributed to Bireswar Basu-Mallick.

4 recordsLinked to original sources

arXiv2024

A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality

We introduce a novel family of translationally-invariant su$(m|n)$ supersymmetric spin chains with long-range interaction not directly associated to a root system. We study the symmetries of these models, establishing in particular the existence of a boson-fermion duality characteristic of this type of systems. Taking advantage of the relation of the new chains with an associated many-body supersymmetric spin dynamical model, we are able to compute their partition function in closed form for all values of $m$ and $n$ and for an arbitrary number of spins. When both $m$ and $n$ are even, we show that the partition function factorizes as the product of the partition functions of two supersymmetric Haldane-Shastry spin chains, which in turn leads to a simple expression for the thermodynamic free energy per spin in terms of the Perron eigenvalue of a suitable transfer matrix. We use this expression to study the thermodynamics of a large class of these chains, showing in particular that the specific heat presents a single Schottky peak at approximately the same temperature as a suitable $k$-level model. We also analyze the critical behavior of the new chains, and in particular the ground state degeneracy and the existence of low energy excitations with a linear energy-momentum dispersion relation. In this way we are able to show that the only possible critical chains are the ones with $m=0,1,2$. In addition, using the explicit formula for the partition function we are able to establish the criticality of the su$(0|n)$ and su$(2|n)$ chains with even $n$, and to evaluate the central charge of their associated conformal field theory.

cond-mat.stat-mech↗

arXiv2019

Appearance of branched motifs in the spectra of $BC_N$ type Polychronakos spin chains

As is well known, energy levels appearing in the highly degenerate spectra of the $A_{N-1}$ type of Haldane-Shastry and Polychronakos spin chains can be classified through the motifs, which are characterized by some sequences of the binary digits like `0' and `1'. In a similar way, at present we classify all energy levels appearing in the spectra of the $BC_N$ type of Polychronakos spin chains with Hamiltonians containing supersymmetric analogue of polarized spin reversal operators. To this end, we show that the $BC_N$ type of multivariate super Rogers-Szegö (SRS) polynomials, which at a certain limit reduce to the partition functions of the later type of Polychronakos spin chains, satisfy some recursion relation involving a $q$-deformation of the elementary supersymmetric polynomials. Subsequently, we use a Jacobi-Trudi like formula to define the corresponding $q$-deformed super Schur polynomials and derive a novel expression for the $BC_N$ type of multivariate SRS polynomials as suitable linear combinations of the $q$-deformed super Schur polynomials. Such an expression for SRS polynomials leads to a complete classification of all energy levels appearing in the spectra of the $BC_N$ type of Polychronakos spin chains through the `branched' motifs, which are characterized by some sequences of integers of the form $(δ_1, δ_2,..., δ_{N-1}|l)$, where $δ_i \in \{ 0,1 \}$ and $ l \in \{ 0,1,...,N \}$. Finally, we derive an extended boson-fermion duality relation among the restricted super Schur polynomials and show that the partition functions of the $BC_N$ type of Polychronakos spin chains also exhibit similar type of duality relation.

cond-mat.stat-mech↗

arXiv2016

Integrable open spin chains related to infinite matrix product states

In this paper we study an su$(m)$-invariant open version of the Haldane-Shastry spin chain whose ground state can be obtained from the chiral correlator of the $c=m-1$ free boson boundary conformal field theory. We show that this model is integrable for a suitable choice of the chain sites depending on the roots of the Jacobi polynomial $P_N^{β-1,β'-1}$, where $N$ is the number of sites and $β,β'$ are two positive parameters. We also compute in closed form the first few nontrivial conserved charges arising from the twisted Yangian invariance of the model. We evaluate the chain's partition function, determine the ground state energy and deduce a complete description of the spectrum in terms of Haldane's motifs and a related classical vertex model. In particular, this description entails that the chain's level density is normally distributed in the thermodynamic limit. We also analyze the spectrum's degeneracy, proving that it is much higher than for a typical Yangian-invariant model.

cond-mat.str-el↗

arXiv2010

One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains

We define a class of $Y(sl_{(m|n)})$ Yangian invariant Haldane-Shastry (HS) like spin chains, by assuming that their partition functions can be written in a particular form in terms of the super Schur polynomials. Using some properties of the super Schur polynomials, we show that the partition functions of this class of spin chains are equivalent to the partition functions of a class of one-dimensional vertex models with appropriately defined energy functions. We also establish a boson-fermion duality relation for the partition functions of this class of supersymmetric HS like spin chains by using their correspondence with one-dimensional vertex models.

cond-mat.stat-mech↗