Quantum lattice models with long-range interactions - phase transitions and ordering patterns

by Dr Jan Koziol (FAU Erlangen)

Tuesday 25 Mar 2025, 11:00 → 12:00 Europe/Zurich

WHGA/121

Quantum lattice models with algebraically decaying long-range interactions are of central interest to many modern quantum simulation platforms. 
Paradigmatic spin systems with long-range interactions can be simulated, among others, in ultra-cold dipolar gases in optical lattices, trapped ions, or Rydberg atoms in optical tweezers.
Therefore, the theoretical understanding of fundamental effects arising from these interactions is essential.

Here, we shed light on two key aspects of these systems providing answers to the following questions:
1. How do long-range interactions influence the nature of quantum phase transitions?
2. How can we calculate magnetically ordered phases arising from long-range interactions?

Long-range interactions provide a path to tune the universal properties of quantum phase transitions.
For example, in ferromagnetic transverse-field Ising models, one can identify three regimes of quantum criticality dependent on the decay of the Ising interactions.
They range from the nearest-neighbor Ising to the long-range mean-field universality classes, with an intermediate non-trivial regime in between.
In the long-range mean-field regime the phase transition is above the upper critical dimension and a special finite-size scaling theory is required.
We present a coherent formalism for finite-size scaling at quantum phase transitions below and above the upper critical dimension, as well as, numerical stochastic series expansion quantum Monte Carlo results for the transverse-field Ising chain.

Antiferromagnetic long-range Ising interactions are known to stabilize a plethora of new magnetically ordered phases compared to nearest-neighbor models. 
In the absence of quantum fluctuations, these phases form a devil's staircase of distinct magnetization plateaux as a function of a longitudinal field.
We present a unit-cell-based approach to numerically determine magnetic ground states for systems with long-range interactions in an unbiased fashion.
Further, we extend this idea to perform mean-field calculations for systems with long-range interactions.
We discuss recent results obtained by this method for the long-range Dicke-Ising model.