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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Minimal Hubbard Models of Maximal Hilbert Space Fragmentation.

Yves H Kwan¹, Patrick H Wilhelm², Sounak Biswas³

¹Princeton University, Princeton Center for Theoretical Science, Princeton, New Jersey 08544, USA.

Physical Review Letters

|February 6, 2025

Summary

Hubbard models with hardcore constraints show maximal Hilbert space fragmentation. This fragmentation leads to anomalous dynamics and emergent symmetries in various lattices, relevant for cold atom experiments.

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Area of Science:

Condensed Matter Physics
Quantum Mechanics
Statistical Mechanics

Background:

Hubbard models are fundamental to understanding interacting quantum systems.
Hilbert space fragmentation can lead to non-ergodic behavior and localization.
Understanding fragmentation is key to predicting system dynamics.

Purpose of the Study:

To investigate Hilbert space fragmentation in Hubbard models with nearest-neighbor hopping and hardcore constraints.
To analyze the impact of fragmentation on system dynamics and emergent symmetries.
To explore the relevance of these findings for experimental systems like optical lattices.

Main Methods:

Analysis of Hubbard models on various lattice dimensions (d=1, d=2).
Focus on the rhombus chain and Lieb lattice.
Explicit construction of emergent integrals of motion and higher-form symmetries.

Main Results:

Demonstration of maximal Hilbert space fragmentation in studied lattices.
Strong fragmentation observed across all fillings in the thermodynamic limit.
Identification of extensive higher-form symmetries and real-space blockades of frozen particles.
Observation of anomalous dynamics due to fragmentation.

Conclusions:

Hubbard models with nearest-neighbor hopping and hardcore constraints exhibit maximal Hilbert space fragmentation.
This fragmentation leads to emergent symmetries and anomalous dynamics.
Results are relevant for quantum simulations using optical lattices with cold atoms.