Algebraic Time Crystallization in a Two-dimensional Superfluid

TL;DR

This paper demonstrates that in two-dimensional superfluids, algebraic time crystallization arises from topological order and temporal phase correlations, with universal decay exponents linked to superfluid stiffness and temperature.

Contribution

It introduces the concept of algebraic time crystallization in 2D superfluids, extending the understanding beyond traditional long-range order to topological order and phase correlations.

Findings

Algebraic decay of temporal phase correlations in 2D superfluids.

Universal relation between decay exponent and superfluid-stiffness-to-temperature ratio.

Proposed experimental protocol to observe time crystallization without continuous contact.

Abstract

Time crystallization is a hallmark of superfluidity, indicative of the fundamental fact that along with breaking the global U(1) symmetry, superfluids also break time-translation symmetry. While the standard discussion of the time crystallization phenomenon is based on the notion of the global phase and genuine condensate, for the superfluidity to take place in two dimensions an algebraic (topological) order is sufficient. We find that the absence of long-range order in a finite-temperature two-dimensional superfluid translates into in an algebraic time crystallization caused by the temporal phase correlations. The exponent controlling the algebraic decay is a universal function of the superfluid-stiffness-to-temperature ratio; this exponent can be also seen in the power-law singularity of the Fourier spectrum of the AC Josephson current. We elaborate on subtleties involved in defining the phenomenon of time crystallization in both classical-filed and all-quantum cases and propose an experimental protocol in which the broken time translation symmetry---more precisely, temporal correlations of the relative phase, with all possible finite-size, dimensional, and quantum effects included---can be observed without permanently keeping two superfluids in a contact.