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arXiv:2012.11521 · Physical Review Research

Experimental characterization of the quantum many-body localization transition

Ming Gong, Gentil D. de Moraes Neto, Chen Zha, Yulin Wu, Hao Rong, Yangsen Ye, Shaowei Li, Qingling Zhu, Shiyu Wang, Youwei Zhao, Futian Liang, Jin Lin, Yu Xu, Cheng-Zhi Peng, Hui Deng, Abolfazl Bayat, Xiaobo Zhu, Jian-Wei Pan

Published Jul 9, 2021• 59 citations
arXivHTMLPDF

Abstract

As strength of disorder enhances beyond a threshold value in many-body systems, a fundamental transformation happens through which the entire spectrum localizes, a phenomenon known as many-body localization. This has profound implications as it breaks down fundamental principles of statistical mechanics, such as thermalization and ergodicity. Due to the complexity of the problem, the investigation of the many-body localization transition has remained a big challenge. The experimental exploration of the transition point is even more challenging as most of the proposed quantities for studying such an effect are practically infeasible. Here, we experimentally implement a scalable protocol for detecting the many-body localization transition point, using the dynamics of an $N=12$ superconducting qubit array. We show that the sensitivity of the dynamics to random samples becomes maximum at the transition point, which leaves its fingerprints in all spatial scales. By exploiting three quantities, each with a different spatial resolution, we identify the transition point with an excellent match between simulation and experiment. In addition, one can detect the evidence of a mobility edge through slight variation of the transition point as the initial state varies. The protocol is easily scalable and can be performed across various physical platforms.

DOI
10.1103/physrevresearch.3.033043

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As strength of disorder enhances beyond a threshold value in many-body systems, a fundamental transformation happens through which the entire spectrum localizes, a phenomenon known as many-body localization. This has profound implications as it breaks down fundamental principles of statistical mechanics, such as thermalization and ergodicity. Due to the complexity of the problem, the investigation of the many-body localization transition has remained a big challenge. The experimental exploration of the transition point is even more challenging as most of the proposed quantities for studying such an effect are practically infeasible. Here, we experimentally implement a scalable protocol for detecting the many-body localization transition point, using the dynamics of an N=12N=12N=12 superconducting qubit array. We show that the sensitivity of the dynamics to random samples becomes maximum at the transition point, which leaves its fingerprints in all spatial scales. By exploiting three quantities, each with a different spatial resolution, we identify the transition point with an excellent match between simulation and experiment. In addition, one can detect the evidence of a mobility edge through slight variation of the transition point as the initial state varies. The protocol is easily scalable and can be performed across various physical platforms.
The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from “extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to “localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder – if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using “quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.
A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site-resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
As disorder strength increases in quantum many-body systems a new phase of matter, the so-called many-body localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that the mid-spectrum eigenstates tend to localize at larger values of disorder in comparison to eigenstates near the edges of the spectrum. Many-body localization becomes more sophisticated in long-range interacting systems. Here, by focusing on several quantities, we draw the phase diagram as a function of disorder strength and energy spectrum, for a various range of interactions. Regardless of the underlying transition type, either second-order or Kosterlitz-Thouless, our analysis consistently determines the mobility edge, i.e., the phase boundary across the spectrum. We show that, long-range interaction enhances the localization effect and shifts the phase boundary towards smaller values of disorder. In addition, we establish a hierarchy among the studied quantities concerning their corresponding transition boundary and critical exponents. Interestingly, we show that deliberately discarding some information of the system can mitigate finite-size effects and provide results in line with the analytical predictions at the thermodynamic limit.
Abstract Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of few-body probes in real space is often insufficient to tackle challenging problems such as quantum critical behavior and many-body localization (MBL) in higher dimensions. Here, we experimentally employ a new paradigm on a superconducting quantum processor, exploring such elusive questions from a Fock space view: mapping the many-body system onto an unconventional Anderson model on a complex Fock space network of many-body states. By observing the wave packet propagating in Fock space and the emergence of a statistical ergodic ensemble, we reveal a fresh picture for characterizing representative many-body dynamics: thermalization, localization, and scarring. In addition, we observe a quantum critical regime of anomalously enhanced wave packet width and deduce a critical point from the maximum wave packet fluctuations, which lend support for the two-dimensional MBL transition in finite-sized systems. Our work unveils a new perspective of exploring many-body physics in Fock space, demonstrating its practical applications on contentious MBL aspects such as criticality and dimensionality. Moreover, the entire protocol is universal and scalable, paving the way to finally solve a broader range of controversial many-body problems on future larger quantum devices.
The failure of quantum thermalization due to Many-Body Localization (MBL) has evolved from a theoretical concept in spin chains to an experimental reality in synthetic quantum platforms, most notably superconducting circuits based on transmon qubits. Despite its significance, the MBL transition has been studied primarily under purely random disorder and local couplings, leaving more complex and realistic configurations largely unexplored. Here, we investigate the quantum dynamics of transmon networks subject to the unavoidable competing effects of correlated disorder and network-mediated non-local interactions. First, we show how to engineer the physical parameters of the quantum hardware to systematically control the correlated disorder patterns emerging in the system. Then, we demonstrate that the MBL phase transition is robust against such correlations, which is essential for tuning localization properties in realistic transmon devices. This robustness is established through the analysis of the block entanglement entropy variance across disorder realizations, which precisely locates the MBL critical point. Independently, we introduce a local memory parameter, whose dynamics at long evolution times reveals memory retention in the localized phase and yields a critical point consistent with the entropy analysis. These results provide a framework for understanding localization in complex quantum network topologies, with potential implications for multi-qubit processor design.