Quantum phase transitions manifest as an abrupt change in the ground state of a many-body system; yet it is an open question whether this sudden change necessarily precludes a continuous dynamical connection between the two phases. We introduce a classification of quantum phase transitions based on this geometric aspect of the ground-state manifold, that differs from known classifications. By leveraging the framework of counterdiabatic driving, we explicitly construct schedules that dynamically connect one phase to another. This strategy allows us to uncover a large class of quantum phase transitions, where the states on both sides are separated only by a finite geometric distance in the thermodynamic limit. We term such transitions traversable, since exact counterdiabatic driving links the two phases via a finite dynamical protocol in the thermodynamic limit. We show that multiple known transitions fall into this class -- e.g., symmetry-breaking transitions obeying hyperscaling and discontinuous transitions with an enhanced continuous symmetry. We further show the existence of quantum phase transitions that cannot be crossed dynamically even with the help of nonlocal counterdiabatic driving, as they would require divergent amplitudes and frequencies. Geometrically, these nontraversable transitions correspond to an infinite distance separating the two phases of matter; we show that the class comprises continuous transitions exhibiting mean-field universality, and discontinuous transitions arising from the competition between metastable minima. Our geometric classification goes beyond the known taxonomy, is independent of local order parameters and renormalization group fixed points, and has direct implications for the complexity of state preparation and adiabatic quantum computation.
Quantum phase transitions manifest as an abrupt change in the ground state of a many-body system; yet it is an open question whether this sudden change necessarily precludes a continuous dynamical connection between the two phases. We introduce a classification of quantum phase transitions based on this geometric aspect of the ground-state manifold, that differs from known classifications. By leveraging the framework of counterdiabatic driving, we explicitly construct schedules that dynamically connect one phase to another. This strategy allows us to uncover a large class of quantum phase transitions, where the states on both sides are separated only by a finite geometric distance in the thermodynamic limit. We term such transitions traversable, since exact counterdiabatic driving links the two phases via a finite dynamical protocol in the thermodynamic limit. We show that multiple known transitions fall into this class -- e.g., symmetry-breaking transitions obeying hyperscaling and discontinuous transitions with an enhanced continuous symmetry. We further show the existence of quantum phase transitions that cannot be crossed dynamically even with the help of nonlocal counterdiabatic driving, as they would require divergent amplitudes and frequencies. Geometrically, these nontraversable transitions correspond to an infinite distance separating the two phases of matter; we show that the class comprises continuous transitions exhibiting mean-field universality, and discontinuous transitions arising from the competition between metastable minima. Our geometric classification goes beyond the known taxonomy, is independent of local order parameters and renormalization group fixed points, and has direct implications for the complexity of state preparation and adiabatic quantum computation.
Quantum materials exhibit rich phenomenology when driven across quantum critical points. Conventional quantum phase transitions are characterized by the change of an order parameter and the emergence of a divergent correlation length. In this work we propose a new class of quantum phase transitions, termed Quantum Matter Causal Phase Transitions (QMCPT), where the underlying causal structure of the many‑body wavefunction reorganizes itself rather than merely the order parameter. We develop a theoretical framework that describes how a causal graph, built from the entanglement structure of the ground state, can undergo a topological change. The transition is marked by a discontinuity or singularity in the causal depth, a quantity that counts the minimal number of layers of local operations required to prepare the state from a product state. We derive scaling relations for the causal depth near criticality, establish its universal behaviour, and discuss possible experimental signatures in strongly correlated systems such as heavy‑fermion compounds and twisted bilayer graphene. The QMCPT framework offers a new classification of quantum phases and provides a bridge between quantum information theory and condensed matter physics, opening pathways for identifying new materials with quantum critical behaviour and potential Nobel‑level discoveries.
We study dynamical phase transitions (DPTs) in quantum many-body systems with infinite-range interaction, and present a theory connecting the two kinds of known DPTs (sometimes referred to as DPTs-I and DPTs-II) with the concept of excited-state quantum phase transition (ESQPT), traditionally found in collective models. We show that DPTs-I appear as a manifestation of symmetry restoration after a quench from the broken-symmetry phase, the limits between these two phases being demarcated precisely by an ESQPT. We describe the order parameters of DPTs-I with a generalization of the standard microcanonical ensemble incorporating the information of two additional conserved charges identifying the corresponding phase. We also show that DPTs-I are linked to a mechanism of information erasure brought about by the ESQPT, and quantify this information loss with the statistical ensemble that we propose. Finally, we show analytically the main mechanism for DPTs-II is forbidden in these systems for quenches leading a broken-symmetry initial state to the same broken-symmetry phase, on one side of the ESQPT, and we provide a formulation of DPTs-II depending on the side of the ESQPT where the quench ends. We analyze the connections between various indicators of DPTs-II. Our results are numerically illustrated in the infinite-range transverse-field Ising model and are applicable to a large class of collective quantum systems satisfying a set of conditions.
Understanding mixed-state quantum phases is a central challenge in the era of quantum simulation, where many existing studies focus on renormalization fixed points. In this work, we move beyond the renormalization fixed-point paradigm by constructing a quantum phase transition connecting two distinct one-dimensional fixed points, both exhibiting finite conditional mutual information and one of which is intrinsically nontrivial. We analytically establish phase equivalence within each of the two phases by explicitly constructing low-depth, quasi-local channel circuits that connect states within each phase. Crucially, our approach leverages the parent Lindbladian construction to generate the desired channel circuits. We further demonstrate that this framework generalizes naturally to a broad class of intrinsically nontrivial mixed-state quantum phases. Our method establishes a framework for rigorously analyzing phase equivalence of intrinsically non-trivial mixed states beyond the renormalization fixed points.
Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce nonlocalquantumfluctuations as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.
Global quenches of quantum many-body models can give rise to periodic dynamical quantum phase transitions (DQPTs) directly connected to the zeros of a Landau order parameter (OP). The associated dynamics has been argued to bear a close resemblance to Rabi oscillations characteristic of two-level systems. Here, we address the question of whether this DQPT behavior is merely a manifestation of the limit of an effective two-level system or if it can arise as part of a more complex dynamics. We focus on quantum many-body scarring as a useful toy model allowing us to naturally study state transfer in an otherwise chaotic system. We find that a DQPT signals a change in the dominant contribution to the wave function in the degenerate initial-state manifold, with a direct relation to an OP zero only in the special case of occurring at the midpoint of an evenly degenerate manifold. Our work generalizes previous results and reveals that, in general, periodic DQPTs comprise complex many-body dynamics fundamentally beyond that of two-level systems.
This manuscript develops a geometric theory of quantum phase transitions that does not begin from a preassigned order parameter, symmetry-breaking pattern, or topological invariant. The basic object is a phase-sensitive state kernel extracted from a ground state, thermal state, band projector, correlation matrix, or quantum geometric tensor. A kernel-resolved phase is defined operationally as a maximal parameter region on which the principal phase-sensitive direction of this kernel can be transported continuously with finite accumulated projective variation. The central diagnostic is the rupture index\kappa=\alpha(1-\beta)=\alpha-\gamma,where \alpha is the local closing exponent of the relevant spectral or kernel separation, \gamma is the independently measured exponent of the transverse carrier amplitude, and \beta=\gamma/\alpha is the relative carrier-amplitude exponent. The theorem-bearing class treated in this paper is the finite-dimensional free-fermion / two-level Dirac-mass class. The transverse-field Ising chain, the SSH chain, and the Kitaev chain are developed as the first model realizations. In all three cases the local channel is a nondegenerate Dirac mass closure with\alpha=1,\qquad \gamma=0,\qquad \beta=0,\qquad \kappa=1.The numerical section is presented as an implementation check of the common local theorem, not as an independent proof of three unrelated mechanisms. A next-harmonic deformation of the SSH model verifies stability under nonuniversal velocity and curvature corrections, while a gapped noncritical control confirms saturation rather than an artificial rupture peak. The paper explicitly delimits BKT, quadratic-touching, multicritical, infinite-dimensional-kernel, interacting-kernel, and non-gap-controlled cases as frontier problems rather than classifying them under the present theorem.