Order Quantum Phase Transition Research Articles

Ferrimagnetic quantum phase transitions and Weyl-Kondo semimetal in a dimerized organic polymer

We study the ferrimagnetic quantum phase transitions (QPTs) and thermodynamics of a dimerized organic polymer, which is described as a periodic Anderson-like model using Green’s function theory. In the absence of magnetic field, it is shown that the Kondo coupling could destroy the Dirac semimetal and induce spin splitting, and the dimerization could open up an energy gap. In a magnetic field, the ferrimagnetic and ferromagnetic insulators as well as Weyl-Kondo semimetal are unveiled. The mechanism of Kondo-singlet competition with dimer-singlet is unveiled to account for the 1/3 magnetization plateau. The field induces second and first order QPTs in the small and large hybridization limit, which is demonstrated by the field scaling of Grüneisen ratio and temperature scaling of specific heat at low temperatures, providing novel thermodynamic means to diagnose the order of QPTs.

Complexity and quenches in models with three and four spin interactions

We study information theoretic quantities in models with three and four spin interactions. These models show distinctive characteristics compared to their nearest neighbour (NN) counterparts. Here, we quantify these in terms of the Nielsen complexity (NC) in static and quench scenarios, the Fubini–Study complexity (FSC), and the entanglement entropy (EE). The models that we study have a rich phase structure, and we show how the difference in the nature of phase transitions in these, compared to ones with NN interactions, result in different behaviour of information theoretic quantities, from ones known in the literature. For example, the derivative of the NC does not diverge but shows a discontinuity near continuous phase transitions, and the FSC may be regular and continuous across such transitions. We also study multiple quench scenarios in these models and contrast these with quenches in the transverse XY model. The EE shows a novel discontinuity both at first and second order quantum phase transitions.

Ferromagnetic instability in itinerant fcc lattice electron systems with higher-order van Hove singularities: Functional renormalization group study

We investigate the possibility of ferromagnetic ordering in the non-degenerate Hubbard model on the face-centered cubic lattice within the functional renormalization group technique using temperature as a scale parameter. We assume the relations between nearest, next-nearest, and next-next-nearest hopping parameters providing higher order (giant) van Hove singularity of the density of states. The ferromagnetic instability formation with lowering temperature is described consistently in the one-loop approximation for a one-particle irreducible vertex of two-particle electron interaction. The chemical potential versus temperature phase diagrams are calculated. We find ferromagnetic order only for sufficiently strong divergence of the density of states and fillings in the vicinity of van Hove singularity. The obtained Curie temperature is more than an order of magnitude smaller than the results of the random-phase approximation. The main origin of the suppression of ferromagnetism is the screening of interaction in the particle-particle channel. We also do not find the pronounced tendency towards incommensurate order when the Fermi level is moved away from a van Hove singularity, such that the first order quantum phase transitions from the ferro- to paramagnetic phase are obtained.

Application of the cranking method to the semimicroscopic algebraic cluster model and nuclear molecules

A particular quantum phase transition (QPT) is studied at excited energies of light nuclei within the Semimicroscopic Algebraic Cluster Model (SACM), using a combination of catastrophe theory and a direct minimization of the potential. A distinct change from a compact nucleus to a nuclear molecule is described as a second order QPT occurring at a certain value of angular momentum. This finding is in accordance with experimental observations when nuclear molecules appear. The method has implication in the fission of heavy nuclei.

Free-Fermionic Topological Quantum Sensors.

Second order quantum phase transitions, with well-known features such as long-range entanglement, symmetry breaking, and gap closing, exhibit quantum enhancement for sensing at criticality. However, it is unclear which of these features are responsible for this enhancement. To address this issue, we investigate phase transitions in free-fermionic topological systems that exhibit neither symmetry-breaking nor long-range entanglement. We analytically demonstrate that quantum enhanced sensing is possible using topological edge states near the phase boundary. Remarkably, such enhancement also endures for ground states of such models that are accessible in solid state experiments. We illustrate the results with 1D Su-Schrieffer-Heeger chain and a 2D Chern insulator which are both experimentally accessible. While neither symmetry-breaking nor long-range entanglement are essential, gap closing remains as the major candidate for the ultimate source of quantum enhanced sensing. In addition, we also provide a fixed and simple measurement strategy that achieves near-optimal precision for sensing using generic edge states irrespective of the parameter value. This paves the way for development of topological quantum sensors which are expected to also be robust against local perturbations.

Breakdown of the Weak-Coupling Limit in Quantum Annealing

Reverse annealing is a variant of quantum annealing, in which the system is prepared in a classical state, reverse-annealed to an inversion point, and then forward-annealed. We report on reverse annealing experiments using the D-Wave 2000Q device, with a focus on the $p=2$ $p$-spin problem, which undergoes a second order quantum phase transition with a gap that closes polynomially in the number of spins. We concentrate on the total and partial success probabilities, the latter being the probabilities of finding each of two degenerate ground states of all spins up or all spins down, the former being their sum. The empirical partial success probabilities exhibit a strong asymmetry between the two degenerate ground states, depending on the initial state of the reverse anneal. To explain these results, we perform open-system simulations using master equations in the limits of weak and strong coupling to the bath. The former, known as the adiabatic master equation (AME), with decoherence in the instantaneous energy eigenbasis, predicts perfect symmetry between the two degenerate ground states, thus failing to agree with the experiment. In contrast, the latter, known as the polaron transformed Redfield equation (PTRE), is in close agreement with experiment. Thus our results present a challenge to the sufficiency of the weak system-bath coupling limit in describing the dynamics of current experimental quantum annealers, at least for reverse annealing on timescales of a microsecond or longer.

Dynamical dephasing of bipartite and tripartite quantum coherence of spin-1/2 XXZ Heisenberg model in a renormalization group approach

The dynamical dephasing of a bipartite and tripartite quantum coherence in spin-1/2 Heisenberg model, driven by an applied magnetic field, in the presence of Dzyaloshinskii-Moriya interaction is investigated. The system is renormalized through the Kadanoof’s blocks approach. It is observed for both bipartite and tripartite schemes that by increasing the size of the system, the quantum coherence measure show an abrupt change at a quantum critical point (QCP). A further increase of the Dzyaloshinskii-Moriya coupling parameter affect the QCP, causing the dynamical dephasing which is the signature of second order quantum phase transition. The displacement of the QCP reduces the Quantum coherence of the system and can be controlled by the external magnetic field strength. Moreover, in a given range of Dzyaloshinskii-Moriya interaction strength and magnetic field, the monogamous and polygamous nature of quantum coherence is related to the size of the system.

Peculiarity of the $${}^{{12}}$$C(0$${{}^{+}}$$) and $${}^{{12}}$$C(2$${{}^{+}}$$) Energy Spectrum in a 3$$\alpha$$ Model

Lowest energy spectrum of the $${}^{12}$$ C nucleus is analyzed in the 3 $$\alpha$$ -cluster model with a deep $$\alpha\alpha$$ potential of Buck, Friedrich and Wheatley with Pauli forbidden states in the $$S$$ and $$D$$ waves. The direct orthogonalization method is applied for the elimination of the 3 $$\alpha$$ Pauli forbidden states. The effects of possible first order quantum phase transition are shown in the lowest $${}^{12}$$ C( $$0_{1}^{+}$$ ) and $${}^{12}$$ C( $$2_{1}^{+}$$ ) states from weakly bound phase to a deep phase. The ground and lowest 2 $${}^{+}$$ states of the $${}^{12}$$ C nucleus in the deep phase are created by the critical eigen states of the Pauli projector for the 0 $${}^{+}$$ and 2 $${}^{+}$$ three-alpha functional spaces, respectively.

Topological Frustration can modify the nature of a Quantum Phase Transition

Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a system's phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.

Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry

We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z2 gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first-order, in contrast to the conventional Z2 lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.

Multiple quantum phase transitions of different nature in the topological kagome magnet Co3Sn2\u2212xInxS2

The exploration of topological electronic phases that result from strong electronic correlations is a frontier in condensed matter physics. One class of systems that is currently emerging as a platform for such studies are so-called kagome magnets based on transition metals. Using muon spin-rotation, we explore magnetic correlations in the kagome magnet Co3Sn2−xInxS2 as a function of In-doping, providing putative evidence for an intriguing incommensurate helimagnetic (HM) state. Our results show that, while the undoped sample exhibits an out-of-plane ferromagnetic (FM) ground state, at 5% of In-doping the system enters a state in which FM and in-plane antiferromagnetic (AFM) phases coexist. At higher doping, a HM state emerges and becomes dominant at the critical doping level of only xcr,1 ≃ 0.3. This indicates a zero temperature first order quantum phase transition from the FM, through a mixed state, to a helical phase at xcr,1. In addition, at xcr,2 ≃ 1, a zero temperature second order phase transition from helical to paramagnetic phase is observed, evidencing a HM quantum critical point (QCP) in the phase diagram of the topological magnet Co3Sn2−xInxS2. The observed diversity of interactions in the magnetic kagome lattice drives non-monotonous variations of the topological Hall response of this system.

Criticality-enhanced quantum sensing in ferromagnetic Bose-Einstein condensates: Role of readout measurement and detection noise

We theoretically investigate estimation of the control parameter in a ferromagnetic Bose-Einstein condensate near second order quantum phase transitions. We quantify sensitivity by quantum and classical Fisher information and using the error-propagation formula. For these different metrics, we find the same, beyond-standard-quantum-limit (SQL) scaling with atom number near critical points, and SQL scaling away from critical points. We find that both depletion of the $m_f=0$ Zeeman sub-level and transverse magnetization provide signals of sufficient quality to saturate the sensitivity scaling. To explore the effect of experimental imperfections, we study the scaling around criticality at nonzero temperature and with nonzero detection noise. Our results suggest the feasibility of sub-SQL sensing in ferromagnetic condensates with current experimental capabilities.

RG flows in non-perturbative gauge-Higgs unification II: effective action for the Higgs phase near the quantum phase transition

We construct the zero temperature (no compact dimensions) effective action for an SU(2) Yang–Mills theory in five dimensions, with boundary conditions that reduce the symmetry on the four-dimensional boundary located at the origin to a U(1)-complex scalar system. In order to be sensitive to the Higgs phase, we need to include higher dimensional operators in the effective action, which can be naturally achieved by generating it by expanding the corresponding lattice construction in small lattice spacing, taking the naive continuum limit and then renormalizing. In addition, we build in the effective action non-perturbative information, related to a first order quantum phase transition known to exist. As a result, the effective action acquires a finite cut-off that is low and the fine tuning of the scalar mass is rather mild.

Superradiance, bosonic Peierls distortion, and lattice gauge theory in a generalized Rabi-Hubbard chain

We investigate a one-dimensional Rabi-Hubbard type of model, arranged such that a qdot is sandwiched between every cavity. The role of the qdot is to transmit photons between neighboring cavities, while simultaneously acting as a photon non-linearity. We consider three-level qdots in the $\Lambda$ configuration, where the left and right leg couples exclusively to the left or right cavity. This non-commuting interaction leads to two highly entangled incompressible phases, separated by a second order quantum phase transition: the qdot degrees-of-freedom act as a dynamical lattice for the photons and a Peierls instability breaks a second $\mathbb{Z}_2$ symmetry which leads to a dimerization in entanglement and photon number. We also find a normal insulating phase and a superfluid phase that acts as a quantum many-body superradiant phase. In the superradiant phase, a $\mathbb{Z}_2$ symmetry is broken and the phase transition falls within the transverse field Ising model universality class. Finally, we show that a limit of the model can be interpreted as a $\mathbb{Z}_2$ lattice gauge theory.

Identifying quantum phase transitions via geometric measures of nonclassicality

In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of nonclassicality are sufficient conditions to identify phase transitions at arbitrary temperature. This establishes that geometric measures of nonclassicality, in any quantum resource theory, are generic tools to investigate phase transitions in quantum systems. At zero temperature, we show that geometric measures of quantum coherence are especially useful for identifying first order quantum phase transitions, and can be a particularly robust alternative to other approaches employing measures of quantum correlations.

Genuine multipartite correlations distribution in the criticality of the Lipkin-Meshkov-Glick model

Correlations play a key role in critical phenomena. Quantities such as the entanglement entropy, for instance, provide key insights into the mechanisms underlying quantum criticality. Almost all of our present knowledge, however, is restricted to bipartite correlations. Some questions still remain unanswered, such as: What parcel of the total correlations are genuinely $k$-partite? With the goal of shedding light on this difficult question, in this paper we put forth a detailed study of the behavior of genuine multipartite correlations (GMC) of arbitrary orders in the Lipkin-Meshkov-Glick model. We find that GMC of all orders serve to signal the second order quantum phase transition presented in the model. Applying finite-size scaling methods, we also find the critical exponents for some orders of correlations.

Integrable model of a p -wave bosonic superfluid

We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.

Topological bound modes in anti-PT-symmetric optical waveguide arrays.

We investigate the topological bound modes in a binary optical waveguide array with anti-parity-time (PT) symmetry. The anti-PT-symmetric arrays are realized by incorporating additional waveguides to the bare arrays, such that the effective coupling coefficients are imaginary. The systems experience two kinds of phase transition, including global topological order transition and quantum phase transition. As a result, the system supports two kinds of robust bound modes, which are protected by the global topological order and the quantum phase, respectively. The study provides a promising approach to realizing robust light transport by utilizing mediating components.

Ising in a transverse field with added transverse Dzyaloshinskii-Moriya interaction

Abstract In this paper, a one-dimensional spin-1/2 Ising model in a transverse magnetic field (ITF) with added the transverse Dzyaloshinskii-Moriya (DM) interaction is considered. The Hamiltonian is exactly diagonalized using the fermionization approach. The energy spectrum, the magnetization and the chiral order parameter are calculated in the thermodynamic limit of the system. In the absence of the transverse magnetic field, a second order quantum phase transition into the chiral ordered phase is happened. In presence of the transverse magnetic field, the quantum critical point is changed. Based on obtained results, three phases named chiral, Neel and ferromagnetic are distinguished and the ground state phase diagram has been plotted. In addition to the response functions, the entanglement and the quantum discord between nearest and next to nearest pair of spins are also investigated. Regarding the quantum correlations, the existence of different ground state phases has been confirmed.

Phase transitions and gaps in quantum random energy models

By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and continuous. We rigorously establish the existence of a universal first order quantum phase transition, obeyed by both the ground and the first excited states. The presence of an exponentially vanishing minimal gap at the transition is general but, quite interestingly, the gap averaged over the realizations of the random potential is finite. This fact leaves still open the chance for some effective quantum annealing algorithm, not necessarily based on a quantum adiabatic scheme.