Quantum Breakdown Condensate Achieves Finite Entropy Density, Demonstrating Disorder-Free Glass Behaviour

The behaviour of quantum systems when pushed to their limits remains a fundamental question in physics, and recent work by Yu-Min Hu, Zhaoyu Han, and Biao Lian from Princeton University, et al., sheds new light on this challenge. These researchers investigate a one-dimensional model exhibiting a unique phenomenon, termed a breakdown condensate, where spontaneous symmetry breaking occurs in an unexpected way. Their findings demonstrate the creation of a novel state of matter, distinct from previously known classifications, that behaves like a quantum glass but without the need for disorder. This achievement, verified through detailed calculations and theoretical analysis, reveals a system with a surprising number of ground states and random internal order, potentially offering new avenues for exploring the foundations of quantum mechanics and materials science.

We study the phase diagram of a one-dimensional spin quantum breakdown model, which possesses an exponential U(1) symmetry with charge unit decaying with site position. Using exact diagonalization, the team demonstrates that the model with spin S ≥ 2 exhibits an exponential U(1) spontaneous symmetry breaking (SSB) phase.

A quantum breakdown condensate exhibits a bulk gap, violating the Goldstone theorem, and an edge mode appearing only on one side when the system has open boundary conditions. Within a lattice of length L, the condensate possesses O(2L) spontaneous symmetry breaking modes.

Many-Body Localization and Spin Chain Dynamics

This supplemental material details supporting evidence for research investigating many-body localization, glassy dynamics, and phase transitions in spin chains. The core research explores whether a spin chain model exhibits many-body localization, a phase where interactions prevent thermalization and the system remains localized even at finite temperatures. Researchers also examine the system’s dynamics, searching for signatures of glassy behavior, and investigate the transition between the localized and thermal phases, considering the impact of boundary conditions.

The study utilizes a spin chain, a one-dimensional system of interacting spins, and restricts calculations to specific charge sectors to simplify analysis. Exact diagonalization, a numerical method for determining energy eigenvalues, is employed for relatively small system sizes. Autocorrelation functions measure how physical quantities, such as spin, change over time, with slowly decaying functions indicating slow dynamics characteristic of glassy systems.

The ground state manifold, the set of lowest-energy states, can be highly degenerate in disordered systems. Researchers analyze the bandwidth, the range of energies within this manifold, and the bulk excitation gap, the energy difference between the ground state and the first excited state. They also consider the Pomeranchuk effect, where thermal fluctuations can replace a continuous phase transition with a crossover, and the Landau-Peierls instability, which suggests thermal fluctuations destroy long-range order at finite temperature.

The team demonstrates the robustness of the observed transition, showing it is not sensitive to changes in the model’s parameters. Colormaps of heat capacity provide further evidence for a finite-temperature crossover, revealing a peak indicating a change in the system’s behavior. Analysis of autocorrelation functions, specifically CXX(t) and CZZ(t), probes the spin dynamics, revealing slow oscillations within the degenerate ground state manifold and fast decay due to excitations outside it.

The results confirm a robust transition or crossover and provide strong evidence for glassy dynamics, with slow relaxation of the x-component of the spin suggesting the system becomes trapped in non-equilibrium states. Differences between periodic and open boundary conditions are primarily at the boundaries, consistent with expectations for physical systems with local interactions. The findings support a finite-temperature crossover, indicating thermal fluctuations prevent a true phase transition.

This work contributes to the understanding of many-body localization, disordered systems, glassy systems, and quantum information. It provides further evidence for the existence of many-body localization and sheds light on the behavior of quantum systems with disorder. The research offers insights into the dynamics of glassy systems and has implications for developing robust quantum memories and quantum computation.

Breakdown Condensate and Exponential Ground State Scaling

This research establishes the existence of a breakdown condensate, a novel quantum state of matter, within a one-dimensional spin model exhibiting exponential symmetry. Through exact diagonalization, scientists demonstrate that the model undergoes spontaneous symmetry breaking, resulting in a unique condensate characterized by a bulk energy gap and an edge mode appearing only on one side. The number of distinct ground states within the condensate scales exponentially with system length, leading to a finite entropy density and a first-order symmetry breaking transition.

The condensate’s order parameter, representing local spin orientation, exhibits effectively random behavior governed by a chaotic relationship, and displays persistent local correlations without establishing long-range order. This combination of properties positions the breakdown condensate as a disorder-free quantum glass, distinct from previously known phases of matter and challenging existing classifications. The authors acknowledge the model’s complex Hilbert space and limited operator connectivity present challenges for understanding its equilibration and categorization as a standard quantum phase, and suggest future investigations could explore potential experimental realizations using platforms like Rydberg atoms, and further examine its implications for quantum information storage and processing, where the condensate’s robustness against local errors may prove advantageous.