2018
DOI: 10.1088/1742-5468/aaa37d
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Phase structure of XX0 spin chain and nonintersecting Brownian motion

Abstract: We study finite size and temperature XX0 Heisenberg spin chain in weak and strong coupling regimes. By using an elegant connection of the model to integrable combinatorics and probability, we explore and interpret a possible phase structure of the model in asymptotic limit: the limit of large inverse temperature and size. First, the partition function and free energy of the model are derived by using techniques and results from random matrix models and nonintersecting Brownian motion. We show that, in the asym… Show more

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Cited by 8 publications
(25 citation statements)
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“…In contrast, because of a correspondence between the XX0 model and Non-Intersecting Brownian Motion (NIBM) [3], this model faces a rather rare third-order phase transition [1], [9]. In our previous study, we explored the phase structure of XX0 spin chain and despite its simplicity we found a sophisticated phase structure for this model [1]. In this study, we generalize the model, in the simplest way, to a long-range interacting model and in the light of the simplicity of the model, we conjecture universality features in the phase structure of the generalized model arising from the conjectural universality of Tracy-Widom distribution (TW) [10], [11], [12].…”
Section: Introductionmentioning
confidence: 98%
See 4 more Smart Citations
“…In contrast, because of a correspondence between the XX0 model and Non-Intersecting Brownian Motion (NIBM) [3], this model faces a rather rare third-order phase transition [1], [9]. In our previous study, we explored the phase structure of XX0 spin chain and despite its simplicity we found a sophisticated phase structure for this model [1]. In this study, we generalize the model, in the simplest way, to a long-range interacting model and in the light of the simplicity of the model, we conjecture universality features in the phase structure of the generalized model arising from the conjectural universality of Tracy-Widom distribution (TW) [10], [11], [12].…”
Section: Introductionmentioning
confidence: 98%
“…Among the variety of classical, quantum and topological phase transitions that occur in XYZ models, the XX0 model does not experience those types of transitions. In contrast, because of a correspondence between the XX0 model and Non-Intersecting Brownian Motion (NIBM) [3], this model faces a rather rare third-order phase transition [1], [9]. In our previous study, we explored the phase structure of XX0 spin chain and despite its simplicity we found a sophisticated phase structure for this model [1].…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations