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Finite-Temperature Screening of U(1) Fractons

Michael Pretko

TL;DR

This work analyzes finite-temperature screening in a three-dimensional U(1) fracton spin liquid described by a rank-2 tensor gauge theory with Gauss's law $\\partial_i\\partial_j E^{ij}=\\rho$. It shows two distinct temporal screening regimes: a weak-screening regime where mobile dipoles partially screen a test charge (with $\\lambda \\propto e^{m_d/2T}$ and $E_{ij} \\sim 1/r^3$), and a strong-screening regime where fracton-on-fracton screening yields exponential decay with $\\lambda \\propto e^{m_f/4T}$ and a long timescale $\\tau_{ss} \\propto e^{(m_f/4+m_d)/T}$. The analysis reveals that, at long times, fractons form neutral composites that move only very slowly, implying slow thermalization and a smooth finite-temperature crossover to a trivial phase, while residual power-law correlations at intermediate times provide a diagnostic for experimental detection of U(1) fracton phases. The paper also discusses extensions to other higher-rank U(1) spin liquids, including Type 2 fracton models and subdimensional phases without fractons, highlighting how mobility and conservation laws shape screening and thermalization across the phase space.

Abstract

We investigate the finite-temperature screening behavior of three-dimensional U(1) spin liquid phases with fracton excitations. Several features are shared with the conventional U(1) spin liquid. The system can exhibit spin liquid physics over macroscopic length scales at low temperatures, but screening effects eventually lead to a smooth finite-temperature crossover to a trivial phase at sufficiently large distances. However, unlike more conventional U(1) spin liquids, we find that complete low-temperature screening of fractons requires not only very large distances, but also very long timescales. At the longest timescales, a charged disturbance (fracton) will acquire a screening cloud of other fractons, resulting in only short-range correlations in the system. At intermediate timescales, on the other hand, a fracton can only be partially screened by a cloud of mobile excitations, leaving weak power-law correlations in the system. Such residual power-law correlations may be a useful diagnostic in an experimental search for U(1) fracton phases.

Finite-Temperature Screening of U(1) Fractons

TL;DR

This work analyzes finite-temperature screening in a three-dimensional U(1) fracton spin liquid described by a rank-2 tensor gauge theory with Gauss's law . It shows two distinct temporal screening regimes: a weak-screening regime where mobile dipoles partially screen a test charge (with and ), and a strong-screening regime where fracton-on-fracton screening yields exponential decay with and a long timescale . The analysis reveals that, at long times, fractons form neutral composites that move only very slowly, implying slow thermalization and a smooth finite-temperature crossover to a trivial phase, while residual power-law correlations at intermediate times provide a diagnostic for experimental detection of U(1) fracton phases. The paper also discusses extensions to other higher-rank U(1) spin liquids, including Type 2 fracton models and subdimensional phases without fractons, highlighting how mobility and conservation laws shape screening and thermalization across the phase space.

Abstract

We investigate the finite-temperature screening behavior of three-dimensional U(1) spin liquid phases with fracton excitations. Several features are shared with the conventional U(1) spin liquid. The system can exhibit spin liquid physics over macroscopic length scales at low temperatures, but screening effects eventually lead to a smooth finite-temperature crossover to a trivial phase at sufficiently large distances. However, unlike more conventional U(1) spin liquids, we find that complete low-temperature screening of fractons requires not only very large distances, but also very long timescales. At the longest timescales, a charged disturbance (fracton) will acquire a screening cloud of other fractons, resulting in only short-range correlations in the system. At intermediate timescales, on the other hand, a fracton can only be partially screened by a cloud of mobile excitations, leaving weak power-law correlations in the system. Such residual power-law correlations may be a useful diagnostic in an experimental search for U(1) fracton phases.

Paper Structure

This paper contains 12 sections, 48 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Conventional $U(1)$ Spin Liquid: A Review
  3. The $U(1)$ Fracton Phase
  4. Review of the Model
  5. Weak-Screening Regime
  6. Absorptive Diffusion
  7. Strong-Screening Regime
  8. Thermalization
  9. Extensions to Other Higher Rank $U(1)$ Spin Liquids
  10. "Type 2" $U(1)$ Fracton Models
  11. Subdimensional Phases without Fractons
  12. Conclusion

Figures (1)

  • Figure 1: A fracton cannot move by itself. However, by absorbing a $\hat{p}$-oriented dipole, the fracton can hop a certain distance in the $\hat{p}$ direction.