# Quantum Time Crystals from Hamiltonians with Long-Range Interactions

## TL;DR

This paper proposes a new Hamiltonian model with long-range interactions that enables the realization of quantum time crystals in closed systems, breaking continuous time-translational symmetry and connecting it to discrete cases.

## Contribution

It introduces a Hamiltonian with long-range multispin interactions that allows for stable quantum time crystals in closed systems, bypassing previous no-go theorems.

## Key findings

- Quantum time crystals are stable at zero temperature.
- The model breaks continuous time-translational symmetry.
- It links continuous and discrete TTS in quantum systems.

## Abstract

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be impossible. In this study we propose a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS. This is based on spin-1/2 many-body Hamiltonian which has long-range multispin interactions in the form of spin strings, thus bypassing previously known no-go theorems. We show that quantum time crystals are stable to local perturbations at zero temperature. Finally, we reveal the intrinsic connection between continuous and discrete TTS, thus linking the two realms.