Measurement induced non-equilibrium phase transitions in many-body quantum systems
Abstract
This proposal theoretically explores non-equilibrium quantum phase transitions that are driven by locally measuring quantum many-body systems at a finite rate. Recent breakthroughs in the dynamics of monitored quantum systems have revealed a novel non-equilibrium phase transition in the many-body wavefunction between thermal, highly entangled states and unentangled, non-ergodic states by increasing the rate of local measurements. This transition arises due to the competition between entangling unitary dynamics and unentangling local projective measurements. At the measurement induced phase transition (MIPT), a Lorentz symmetry emerges with universal entanglement dynamics. Broadly speaking, this work seeks to develop a fundamental understanding of the MIPT, which has implications for quantum computing in noisy intermediate scale quantum technologies, quantum error correction, quantum information, and fundamental questions in non-equilibrium quantum statistical mechanics. The specific objectives of this proposal are to: (i) use static disorder to destabilize the Lorentz invariant MIPT to discover novel non-equilibrium phase transitions, (ii) determine the effects of a continuous symmetry and the resulting conservation law on the MIPT, and (iii) demonstrate that for integrable quantum dynamics the existence of the MIPT is sensitive to the measurement basis. Our proposed research utilizes a cross fertilization of ideas from statistical physics, critical phenomena, quantum information, and computational physics. The non-unitary time evolution of random quantum circuit models with measurements will be simulated numerically using a variety of techniques. In particular, the methods employed in this proposal include simulating stabilizer circuits with classical efficiency, Chebyshev expansions and sparse-matrix vector approaches, matrix-product state representations, and solutions of the stochastic Schrodinger equation. The ultimate goal of this research proposal is to determine how the MIPT is fundamentally altered by incorporating realistic physical phenomena that is known to change the entangling unitary dynamics. In (i), we will demonstrate that the MIPT is unstable to static disorder and flows to a novel critical point that may represent a unique infinite randomness fixed point in the absence of unitarity. The outcome of this finding is essential to construct a general scaling theory description of the MIPT, which predicts the outcome of problems in far more general settings and higher dimensions. The calculations in (ii) will determine the stability of diffusion to disentangling measurements that will lead to fundamental insights into the nature of symmetry, conservation laws, and the observer. Last, the investigations in (iii) will uncover the fragility of integrable quantum many-body systems to a non-zero measurement rate and determine the role of the measurement basis on the existence of the MIPT. The successful completion of this proposal will transform our understanding of non-equilibrium quantum phase transitions that are driven by local measurements in a wide variety of many-body quantum systems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 19, 2023
- Source ID
- W911NF2310144
Entities
People
- Jedediah H Pixley
Organizations
- Army Contracting Command
- Rutgers University
- United States Army