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We study the thermodynamics and critical behavior of su($m|n$) supersymmetric spin chains of Haldane-Shastry type with a chemical potential term. We obtain a closed-form expression for the partition function and deduce a description of the spectrum in terms of the supersymmetric version of Haldanes motifs, which we apply to obtain an analytic expression for the free energy per site in the thermodynamic limit. By studying the low-temperature behavior of the free energy, we characterize the critical behavior of the chains with $1le m,nle2$, determining the critical regions and the corresponding central charge. We also show that in the su($2|1$), su($1|2$) and su($2|2$) chains the bosonic or fermionic densities can undergo first-order (discontinuous) phase transitions at $T=0$, in contrast with the previously studied su(2) case.
We analyze the thermodynamics and the critical behavior of the supersymmetric su($m$) $t$-$J$ model with long-range interactions. Using the transfer matrix formalism, we obtain a closed-form expression for the free energy per site both for a finite n
The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin model
Using an infinite Matrix Product State (iMPS) technique based on the time-dependent variational principle (TDVP), we study two major types of dynamical phase transitions (DPT) in the one-dimensional transverse-field Ising model (TFIM) with long-range
The existence or absence of non-analytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. H
We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and (polarized) spin reversal operators, which includes the Haldane-Shastry chain as a particular degenerate case.