Multipartite entanglement lies at the heart of quantum many-body physics and quantum information science, serving as a key resource for quantum computation, quantum simulation, and quantum metrology. While its behavior in Hermitian systems has been extensively studied, its fate in non-Hermitian systems, especially those with synthetic gauge fields, remains largely unexplored. In this work we investigate multipartite entanglement dynamics in a quadruple-well system under the influence of synthetic gauge fields and nonreciprocal coupling. By constructing a many-body Hamiltonian that incorporates synthetic gauge fluxes, interaction-induced nonlinearity, and parity-time ($\mathcal{PT}$) symmetry-breaking terms, we reveal that the interplay between non-Hermiticity and gauge fields provides unprecedented control over entanglement structures and their evolution. Notably, the synthetic gauge field acts as a tunable switch for entanglement configurations, enabling transitions between separable, bipartite, tripartite, and globally entangled configurations. Furthermore, we uncover a striking odd-even effect of particle number on both $\mathcal{PT}$-symmetry phase transitions and entanglement patterns, highlighting the role of particle-number parity in non-Hermitian many-body systems. These findings not only deepen our understanding of many-body quantum correlations in non-Hermitian systems but also open alternative avenues for designing entanglement-resolved quantum sensors and preparing topologically nontrivial many-body states in synthetic quantum platforms.
Multipartite entanglement lies at the heart of quantum many-body physics and quantum information science, serving as a key resource for quantum computation, quantum simulation, and quantum metrology. While its behavior in Hermitian systems has been extensively studied, its fate in non-Hermitian systems, especially those with synthetic gauge fields, remains largely unexplored. In this work we investigate multipartite entanglement dynamics in a quadruple-well system under the influence of synthetic gauge fields and nonreciprocal coupling. By constructing a many-body Hamiltonian that incorporates synthetic gauge fluxes, interaction-induced nonlinearity, and parity-time (PT) symmetry-breaking terms, we reveal that the interplay between non-Hermiticity and gauge fields provides unprecedented control over entanglement structures and their evolution. Notably, the synthetic gauge field acts as a tunable switch for entanglement configurations, enabling transitions between separable, bipartite, tripartite, and globally entangled configurations. Furthermore, we uncover a striking odd-even effect of particle number on both PT-symmetry phase transitions and entanglement patterns, highlighting the role of particle-number parity in non-Hermitian many-body systems. These findings not only deepen our understanding of many-body quantum correlations in non-Hermitian systems but also open alternative avenues for designing entanglement-resolved quantum sensors and preparing topologically nontrivial many-body states in synthetic quantum platforms.
Out-of-equilibrium quantum many-body systems stand at the forefront of modern theoretical physics, addressing fundamental questions on thermalization, transport, and universal phenomena. These fields, already well established in condensed matter, statistical physics, quantum optics, and quantum information theory, are progressively gaining even greater relevance with the rapid development of quantum technologies and simulation, which inherently operate in dynamical regimes. In recent years, the traditional paradigm of unitary quantum evolution has been expanded to include measurements, opening new directions in out-of-equilibrium physics. At the core of these advances lie measurement-induced phase transitions (MIPTs), which have emerged as a new class of dynamical critical phenomena characterizing the general behavior of monitored quantum dynamics. When external monitoring intertwines with unitary evolution, many-body quantum correlations change their structure, giving rise to distinct entanglement phases of matter. This discovery has sparked enormous interest in MIPTs, leading to significant advances in open quantum systems, entanglement theory, and more broadly quantum complexity. Despite much progress, a full understanding of monitored many-body dynamics is far from complete, leaving several open questions on the nature of MIPTs, their experimental observability, and the possibilities offered by measurements to enhance control over synthetic quantum matter. These issues persist due to the intrinsic complexity of the problem and the lack of efficient tools to study it, mainly caused by the stochastic character of monitored evolution. This thesis addresses these challenges by expanding the investigation of measurement-induced phenomena in new settings and introducing innovative probes of entanglement and many-body quantum complexity for MIPTs. A core question we investigate is the role of symmetries, non-ergodicity, and especially integrability in measurement-induced criticality, which dramatically affect the non-equilibrium phases. We further explore how these phenomena extend beyond bipartite quantum correlations to multipartite entanglement and quantum non-stabilizerness, highlighting the non-trivial interplay between measurements and complexity notions rooted in quantum information theory. Finally, we focus on the compelling problem of decoherence, modeling how noise spoils entanglement structures. These findings, supported by advanced numerical simulations and theoretical analysis, deepen the current understanding of entanglement, complexity, and integrability in monitored quantum many-body systems, offering new perspectives on their rich behavior. In parallel, we address the experimental problem of dissipation in MIPTs, which is of key relevance for practical implementations. We anticipate the present investigation to foster future research on the nature of monitored dynamical critical phenomena and, more broadly, the applications of measurements in quantum state evolution.
In this thesis, we study two distinct, yet equally fascinating, aspects of manybody physics. Synthetic quantum matter – engineered many-body systems with high controllability and tunability – serves as a cornerstone for the research. The combination of these features makes them incredibly suited for research at the crossroads of traditional statistical physics, new concepts coming from field theory (particularly gauge theories), and quantum information. In the first part, we delve into the quantum simulation of novel quantum phenomena with analog quantum simulators. In particular, recent advances in the synthetic platforms based on Rydberg atoms, i.e., neutral atoms trapped in optical tweezers, have opened up new avenues to explore exotic topological phases like quantum spin liquids, which hold potential applications in quantum computing. We employ a combination of numerical and analytical tools to address open questions regarding the realization of these phases in experiments. Our results show that the recently observed spin liquids can be directly connected to a Higgs-Ising lattice gauge theory, providing a clear-cut theoretical argument for its origin. Moreover, different setups with chiral interacting Hamiltonians offer new avenues to realize chiral spin liquids - a lattice version of the celebrated quantum Hall effect. In the second part, we explore the role of a quantum information quantity known as nonstabilizerness in quantum many-body systems. By now, the study of quantum information concepts in the realm of many-body theory represents a very active research effort, with a prominent example being entanglement, which has revolutionized our understanding of quantum systems. Similar to entanglement, nonstabilizerness has emerged as a crucial resource for achieving quantum advantage, although in a fundamentally different way. While entanglement is well-studied, the exploration of nonstabilizerness in many-body contexts is still in its very early stages. Its ongoing investigation holds significant promise for deepening our understanding of many-body systems and their complexity. We develop new methods based on tensor networks and Monte Carlo methods to enable the quantification of nonstabilizerness at large scales. We subsequently apply them to uncover the role of nonstabilizerness in various many-body settings, particularly in critical phenomena, gauge theory, and quantum circuits.
The competition between unitary time evolution and quantum measurements could induce phase transitions in the entanglement characteristics of quantum many-body dynamics. In this work, we reveal such entanglement transitions in the context of non-Hermitian Floquet systems. Focusing on noninteracting fermions in a representative bipartite lattice with balanced gain/loss and under time-periodic quenches, we uncover rich patterns of entanglement transitions due to the interplay between driving and non-Hermitian effects. Specially, we find that the monotonic increase of quenched hopping amplitude could flip the system between volume-law and area-law entangled Floquet phases, yielding alternated entanglement transitions. Meanwhile, the increase of gain/loss strength could trigger area-law to volume-law reentrant transitions in the scaling behavior of steady-state entanglement entropy, which are abnormal and highly unexpected in nondriven systems. Connections between entanglement transitions and parity-time-reversal (PT) transitions in Floquet spectra are further established. Our findings not only build a foundation for exploring entanglement phase transitions in Floquet non-Hermitian setups, but also provide efficient means to engineer and control such transitions by driving fields. Published by the American Physical Society 2024
Abstract Non-Hermitian quantum systems showcase many distinct and intriguing features with no Hermitian counterparts. One of them is the exceptional point which marks the PT (parity and time) symmetry phase transition, where an enhanced spectral sensitivity arises and leads to novel quantum engineering. Here we theoretically study the multipartite entanglement properties in non-Hermitian superconducting qubits, where high-fidelity entangled states can be created under strong driving fields or strong couplings among the qubits. Under an interplay between driving fields, couplings, and non-Hermiticity, we focus on generations of GHZ states or GHZ classes in three and four qubits with all-to-all couplings, which allows a fidelity approaching unity when relatively low non-Hermitian decay rates are considered. This presents an ultimate capability of non-Hermitian qubits to host a genuine and maximal multipartite entanglement. Our results can shed light on novel quantum engineering of multipartite entanglement generations in non-Hermitian qubit systems.
Abstract The evolution of entanglement in a non-Hermitian quantum system may behave differently compared to its Hermitian counterpart. In this paper, we investigate the entanglement dynamics of two coupled and driven non-Hermitian qubits. Through calculating the concurrence of the system, we find that the evolution of the bipartite entanglement manifests two distinct patterns in the parameter space. In the low non-Hermiticity regime, the concurrence oscillates significantly, while in the opposite regime the same quantity would trend to a stable value. We attribute this phenomenon to parity-time ( PT ) symmetry phase transition. We also study the effect of decoherence on the entanglement dynamics. Our work provides a method to stabilize entanglement by exploiting non-Hermiticity.
For decades, Hermiticity was considered an immutable axiom of quantum mechanics, essential for ensuring real energies and unitary evolution. This perspective has shifted radically, driven by the realization that non-Hermitian Hamiltonians provide a powerful effective description of open quantum systems, granting access to unique phenomena such as Exceptional Points and the Non-Hermitian Skin Effect. In this Perspective, we chart the trajectory of this field, moving from its established foundations in single-particle, linear models to the emerging frontier of interacting many-body systems. We first clarify the physical origins of non-Hermitian dynamics, distinguishing between mean-field approximations, conditional "no-click" evolution, and exact Liouvillian dynamics. We then focus on the rich phenomenology arising from the interplay of non-Hermiticity and interactions. We discuss interaction-induced topological phases, the generalization of skin effects to the many-body Hilbert space, and the distinct signatures of dissipative quantum chaos and complexity. Finally, we highlight collective phenomena in nonlinear regimes, including skin solitons and dissipative phase transitions. We also comment on measurement-induced entanglement transitions and their relation to non-Hermitian spectra and topology. By synthesizing these diverse developments, we provide a roadmap for the future of non-Hermitian physics.