Finite-temperature criticality in systems with power-law interactions
Shijun Sun, Sergey Syzranov
In preparation
We study the critical behavior of a dilute gas of bosons with power-law dispersion at finite temperatures. We apply the field theoretic renormalization group analysis and find that for particles with attractive interactions exhibit a phase transition in dimensions higher than the critical dimension. To seek a concrete example, we study a spin model with long-range interactions, whose elementary excitations are power-law dispersing bosons with attractive interactions. The spin model can be realized, and the phase transition can be detected, in trapped-ion experiments. The phase transition is similar to a type of non-Anderson disorder-driven phase transition, which is not a coincidence but is predicted by the interaction — disorder duality that we established in previous work (see the third work below).
Quasispins of vacancy defects in Ising chains with nearest- and next-to-nearest-neighbour interactions
Shijun Sun, Arthur P. Ramirez, Sergey Syzranov
This work is motivated by the interesting effects of vacancy defects (i.e., non-magnetic impurity) in geometrically frustrated magnets. Namely, it introduces a free spin degree of freedom — a quasispin. We study a simple toy model, 1D Ising model with nearest- and next-to-nearest-neighbor interactions, which gives non-trivial effects of vacancies and captures some of the effects of frustration.
We found the effect of vacancy defects on magnetic susceptibility is two-fold: a) it acts as a free spin — quasispin; b) it reduces the length of the chain by an effective “vacancy size”. You can read more about our work from our paper or this poster I made.
Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
Shijun Sun, Sergey Syzranov
We derived an equivalence between two rather different types of systems: clean systems with interactions between quasiparticles and systems in which the particles are in random potentials (quenched disorders) and are not interacting with each other. This result is powerful: on the one hand, it allows us to study certain types of many-body problems by mapping them to single-body problems in random potentials; on the other hand, new phenomena in systems with quenched disorder can be found by mapping well-studied interaction phenomena to them. As an example, we found a new type of disorder-driven phase transition in systems with quenched disorders by mapping an interaction-driven phase transition, the BEC-vacuum transition for power-law dispersing bosons, using the derived duality. You can read more about the duality mapping in our paper.
Obstacles in constructing de Sitter space in String theory
Michael Dine, Jamie A.P. Law-Smith, Shijun Sun, Duncan Wood, Yan Yu*
The aim of this project was to reveal the limitations of String theory in constructing de Sitter spaces. Why should we care? Because our universe is a de Sitter space — it has uniform positive cosmological constant. However, it turns out to be hard to construct de Sitter space from String theory. We completed calculations using quantum field theory to reveal the major obstacles that hinder string theory from constructing de Sitter spaces. The obstacles are as follows. 1. De Sitter space, if it exists in string theory solutions, must lie in the non-perturbative regime; 2. de Sitter space necessarily breaks supersymmetry, and without supersymmetry, one loses non-perturbative control; 3. de Sitter space is, at best, metastable, and the decay of it leads to singularities in the effective field theory. You can read more about our work from our paper.
*Authors are ordered alphabetically
Talks
Universal quasiparticle dynamics in systems with power-law interaction
APS March Meeting – March 2023 [slides]
Based on work in preparation
Interaction-disorder duality and unconventional phase transitions for nodal-semimetals and ultracold gases
APS March Meeting – March 2022 [slides]
Based on work found in arXiv:2104.02720
Unconventional phase transitions in disordered and dissipative systems
1-hour talk at UC Santa Cruz Condensed Matter Seminar – October 2021 [slides]
Based on work found in arXiv:2104.02720