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Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids (1604.05329v3)

Published 18 Apr 2016 in cond-mat.str-el and hep-th

Abstract: Spin liquids are conventionally described by gauge theories with a vector gauge field. However, there exists a wider class of spin liquids with higher rank tensors as the gauge variable. In this work, we focus on (3+1)-dimensional spin liquids described by U(1) symmetric tensor gauge theories, which have recently been shown to be stable gapless spin liquids. We investigate the particle structure of these tensor gauge theories and find that they have deep connections with the "fracton" models recently discovered by Vijay, Haah, and Fu. Tensor gauge theories have more conservation laws than the simple charge conservation law of rank 1 theories. These conservation laws place severe restrictions on the motion of particles. Particles in some models are fully immobile (fractons), while other models have particles restricted to motion along lower-dimensional subspaces.

Citations (266)

Summary

  • The paper reveals that higher rank U(1) spin liquids host stable subdimensional excitations, including immobile fractons governed by extra conservation laws.
  • The study employs tensor gauge theories to demonstrate that fracton dynamics and one-dimensional mobility emerge from angular momentum and dipole moment constraints.
  • It shows that divergent electrostatic energy in scalar charge models indicates a new form of confinement with significant implications for experimental quantum systems.

Overview of Subdimensional Particle Structure of Higher Rank U(1)U(1) Spin Liquids

This paper explores the intriguing terrain of higher rank U(1)U(1) spin liquids, characterized by tensor gauge theories, which represent a departure from conventional vector gauge spin liquid models. In particular, it explores the (3+1)-dimensional U(1)U(1) symmetric tensor gauge theories, which are confirmed as stable gapless phases and exhibit complex particle behaviors associated with additional conservation laws, particularly echoing the peculiar features of "fracton" models.

Key Findings and Numerical Results

The paper reveals that in U(1)U(1) symmetric tensor gauge theories, there are profound modifications in particle mobility compared to traditional vector gauge theories. Rank 2 tensor gauge theories give rise to distinct types of subdimensional particles:

  • Fractons: Particles that are completely immobile due to higher-order conservation laws, namely, the conservation of dipole moment along with charge neutrality for scalar charge theories.
  • Subdimensional particles: Particles that can only move within restricted lower-dimensional subspaces, such as one-dimensional propagation for vector charge theories, due to additional topological constraints like angular momentum conservation.

A significant numerical insight is the divergent electrostatic energy associated with isolated point charges in scalar charge models, where the energy stored in these fields scales linearly with system size, indicating a novel form of "electrostatic confinement." This differs from usual Polyakov confinement, presenting particles as stable but energetically costly due to the long-range nature of their electrostatic fields.

Implications and Future Directions

The implications of this work are manifold, influencing both theoretical understanding and potential experimental realizations. The introduction of tensor gauge structures suggests an extension in the classification of long-range entangled phases, potentially bridging connections to theories of quantum gravity due to the tensorial nature of gravitational fields. Practically, these models offer a new class of quantum spin liquids with unconventional excitations that could be observed in experimental settings, particularly within quantum rotor systems or frustrated spin systems.

From a theoretical perspective, this paper raises numerous questions about the potential unification of all fracton models within the framework of tensor gauge theories, and the implications for universality classes of subdimensional matter. Questions regarding non-abelian extensions of these theories, the nature of phase transitions, and the behavior under disequilibria remain open avenues for exploration.

The work presented inspires further investigation into the subdimensional behavior from both a particle dynamics and thermodynamics viewpoint, particularly in connection with thermalization and localization properties in these zero-disorder scenarios.

Conclusion

This paper extends the horizon of quantum spin liquids by establishing higher rank symmetric tensor gauge theories as fertile grounds for subdimensional particle dynamics, with a compelling interplay between conservation laws and particle mobility. While the paper remains largely theoretical, it sets the stage for subsequent experimental efforts to uncover and manipulate such exotic phases of matter, which pose intriguing opportunities for both quantum information and condensed matter physics. Researchers are encouraged to pursue these directions, uncovering deeper insights into the mathematical structures underpinning these novel systems.