Nature Of Quantum Phase Transition Research Articles

Emergent symmetry in quantum phase transition: From deconfined quantum critical point to gapless quantum spin liquid

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the J1x-J1y-J2 model, which contains anisotropic nearest-neighbor couplings J1x,J1y and the next nearest neighbor coupling J2. For small J1y/J1x, by tuning J2, a direct continuous transition between the AFM and valence bond solid phase is observed. With growing J1y/J1x, a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM–VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL–VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.

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.

Correlation-driven electron-hole asymmetry in graphene field effect devices

Electron-hole asymmetry is a fundamental property in solids that can determine the nature of quantum phase transitions and the regime of operation for devices. The observation of electron-hole asymmetry in graphene and recently in twisted graphene and moiré heterostructures has spurred interest into whether it stems from single-particle effects or from correlations, which are core to the emergence of intriguing phases in moiré systems. Here, we report an effective way to access electron-hole asymmetry in 2D materials by directly measuring the quasiparticle self-energy in graphene/Boron Nitride field-effect devices. As the chemical potential moves from the hole to the electron-doped side, we see an increased strength of electronic correlations manifested by an increase in the band velocity and inverse quasiparticle lifetime. These results suggest that electronic correlations intrinsically drive the electron-hole asymmetry in graphene and by leveraging this asymmetry can provide alternative avenues to generate exotic phases in twisted moiré heterostructures.

Quantum phase transitions in Dirac fermion systems

A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention has been paid in recent years to two-dimensional (2D) materials in which itinerant fermions acquire a pseudo-relativistic Dirac dispersion, such as graphene, topological insulator surfaces, and certain spin liquids. This article reviews the phenomenology and theoretical description of quantum phase transitions in systems of 2D Dirac fermions.

A selective control of volatile and non-volatile superconductivity in an insulating copper oxide via ionic liquid gating

Manipulating the superconducting states of high transition temperature (high-Tc) cuprate superconductors in an efficient and reliable way is of great importance for their applications in next-generation electronics. Here, employing ionic liquid gating, a selective control of volatile and non-volatile superconductivity is achieved in pristine insulating Pr2CuO4±δ (PCO) films, based on two distinct mechanisms. Firstly, with positive electric fields, the film can be reversibly switched between superconducting and non-superconducting states, attributed to the carrier doping effect. Secondly, the film becomes more resistive by applying negative bias voltage up to − 4 V, but strikingly, a non-volatile superconductivity is achieved once the gate voltage is removed. Such phenomenon represents a distinctive route of manipulating superconductivity in PCO, resulting from the doping healing of oxygen vacancies in copper-oxygen planes as unravelled by high-resolution scanning transmission electron microscope and in situ X-ray diffraction experiments. The effective manipulation of volatile/non-volatile superconductivity in the same parent cuprate brings more functionalities to superconducting electronics, as well as supplies flexible samples for investigating the nature of quantum phase transitions in high-Tc superconductors.

Quantum Phase Transition in Fully Connected Quantum Wajnflasz–Pick Model

We construct a quantum Wajnflasz-Pick model that is a generalized quantum Ising model, and investigate a nature of quantum phase transitions of the model with infinite-range interactions. Quantum phase transition phenomena have drawn attention in the field of quantum computing as well as condensed matter physics, since the phenomena are closely related to the performance of quantum annealing (QA) and adiabatic quantum computation (AQC). We add a quantum driver Hamiltonian to the Hamiltonian of classical Wajnflasz-Pick model. The classical Wajnflasz-Pick model consists of two-level systems as with the usual Ising model. Unlike the usual Ising spin, each of the upper and the lower levels of the system can be degenerate. The states in the upper level and the lower level are referred to as upper states and lower states, respectively. The quantum driver Hamiltonian we introduced causes spin flip between the upper and the lower states and state transitions within each of the upper and the lower states. Numerical analysis showed that the model undergoes first-order phase transitions whereas a corresponding quantum Ising model, quantum Curie-Weiss model, does not undergo first-order phase transitions. In particular, we observed an anomalous phenomenon that the system undergoes successive first-order phase transitions under certain conditions. The obtained results indicate that the performance of QA and AQC by using degenerate two-level systems can be controlled by the parameters in the systems.

Machine learning of quantum phase transitions

Machine learning algorithms provide a new perspective on the study of physical phenomena. In this Rapid Communication, we explore the nature of quantum phase transitions using a multicolor convolutional neural network (CNN) in combination with quantum Monte Carlo simulations. We propose a method that compresses $(d+1)$-dimensional space-time configurations to a manageable size and then use them as the input for a CNN. We benchmark our approach on two models and show that both continuous and discontinuous quantum phase transitions can be well detected and characterized. Moreover, we show that intermediate phases, which were not trained, can also be identified using our approach.

Evolution of Magnetic Double Helix and Quantum Criticality near a Dome of Superconductivity in CrAs

At ambient pressure CrAs undergoes a first-order transition into a double-helical magnetic state at TN = 265 K, which is accompanied by a structural transition. The recent discovery of pressure-induced superconductivity in CrAs makes it important to clarify the nature of quantum phase transitions out of its coupled structural/helimagnetic order. Here we show, via neutron diffraction on the single-crystal CrAs under hydrostatic pressure (P), that the combined order is suppressed at Pc ~ 10 kbar, near which bulk superconductivity develops with a maximal transition temperature Tc ~ 2 K. We further show that the coupled order is also completely suppressed by phosphorus doping in CrAs1-xPx at a critical xc ~ 0.05, above which inelastic neutron scattering evidenced persistent antiferromagnetic correlations, providing a possible link between magnetism and superconductivity. In line with the presence of antiferromagnetic fluctuations near Pc (xc), the A coefficient of the quadratic temperature dependence of resistivity exhibits a dramatic enhancement as P (x) approaches Pc (xc), around which Res(T) has a non-Fermi-liquid form. Accordingly, the electronic specific-heat coefficient of CrAs1-xPx peaks out around xc. These properties provide clear evidences for quantum criticality, which we interpret as originating from a nearly second-order helimagnetic quantum phase transition that is concomitant with a first-order structural transition. Our findings in CrAs highlight the distinct characteristics of quantum criticality in bad metals, thereby bringing out new insights into the physics of unconventional superconductivity such as occurring in the high-Tc iron pnictides.

Emergence of Quantum Critical Behavior in Metallic Quantum-Well States of Strongly Correlated Oxides

Controlling quantum critical phenomena in strongly correlated electron systems, which emerge in the neighborhood of a quantum phase transition, is a major challenge in modern condensed matter physics. Quantum critical phenomena are generated from the delicate balance between long-range order and its quantum fluctuation. So far, the nature of quantum phase transitions has been investigated by changing a limited number of external parameters such as pressure and magnetic field. We propose a new approach for investigating quantum criticality by changing the strength of quantum fluctuation that is controlled by the dimensional crossover in metallic quantum well (QW) structures of strongly correlated oxides. With reducing layer thickness to the critical thickness of metal-insulator transition, crossover from a Fermi liquid to a non-Fermi liquid has clearly been observed in the metallic QW of SrVO3 by in situ angle-resolved photoemission spectroscopy. Non-Fermi liquid behavior with the critical exponent α = 1 is found to emerge in the two-dimensional limit of the metallic QW states, indicating that a quantum critical point exists in the neighborhood of the thickness-dependent Mott transition. These results suggest that artificial QW structures provide a unique platform for investigating novel quantum phenomena in strongly correlated oxides in a controllable fashion.

Fermion-induced quantum critical points in two-dimensional Dirac semimetals

In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and $Z_3$-ordered phases (e.g. Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first-order. From large-$N$ renormalization group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nature Communications 8, 314 (2017)] occur when $N$ (the number of flavors of four-component Dirac fermions) is larger than a critical value $N_c$. Remarkably, from the knowledge of spacetime supersymmetry, we obtain an exact lower bound for $N_c$, i.e., $N_c>1/2$. (Here the "1/2" flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., $\nu$$\neq$$\nu'$, by large-$N$ RG calculations. We further give a brief discussion on possible experimental realizations of FIQCPs.

Quantum phase transitions of light in a dissipative Dicke-Bose-Hubbard model

The impact that the environment has on the quantum phase transition of light in the Dicke-Bose-Hubbard model is investigated. Based on the quasibosonic approach, mean-field theory, and perturbation theory, the formulation of the Hamiltonian, the eigenenergies, and the superfluid order parameter are obtained analytically. Compared with the ideal cases, the order parameter of the system evolves with time as the photons naturally decay in their environment. When the system starts with the superfluid state, the dissipation makes the photons more likely to localize, and a greater hopping energy of photons is required to restore the long-range phase coherence of the localized state of the system. Furthermore, the Mott lobes depend crucially on the numbers of atoms and photons (which disappear) of each site, and the system tends to be classical with the number of atoms increasing; however, the atomic number is far lower than that expected under ideal circumstances. As there is an inevitable interaction between the coupled-cavity array and its surrounding environment in the actual experiments, the system is intrinsically dissipative. The results obtained here provide a more realistic image for characterizing the dissipative nature of quantum phase transitions in lossy platforms, which will offer valuable insight into quantum simulation of a dissipative system and which are helpful in guiding experimentalists in open quantum systems.

Chiral and critical spin liquids in a spin-12kagome antiferromagnet

The topological quantum spin liquids (SL) and the nature of quantum phase transitions between them have attracted intensive attentions for the past twenty years. The extended kagome spin-1/2 antiferromagnet emerges as the primary candidate for hosting both time reversal symmetry (TRS) preserving and TRS breaking SLs based on density matrix renormalization group simulations. To uncover the nature of the novel quantum phase transition between the SL states, we study a minimum XY model with the nearest neighbor (NN) ($J_{xy}$), the second and third NN couplings ($J_{2xy}=J_{3xy}=J'_{xy}$). We identify the TRS broken chiral SL (CSL) with the turn on of a small perturbation $J'_{xy}\sim 0.06 J_{xy}$, which is fully characterized by the fractionally quantized topological Chern number and the conformal edge spectrum as the $\nu=1/2$ fractional quantum Hall state. On the other hand, the NN XY model ($J'_{xy}=0$) is shown to be a critical SL state adjacent to the CSL, characterized by the gapless spin singlet excitations and also vanishing small spin triplet excitations. The quantum phase transition from the CSL to the gapless critical SL is driven by the collapsing of the neutral (spin singlet) excitation gap. By following the evolution of entanglement spectrum, we find that the transition takes place through the coupling of the edge states with opposite chiralities, which merge into the bulk and become gapless neutral excitations. The effect of the NN spin-$z$ coupling $J_z$ is also studied, which leads to a quantum phase diagram with an extended regime for the gapless SL.

Optical Conductivity Measurement of a Dimer Mott-Insulator to Charge-Order Phase Transition in a Two-Dimensional Quarter-Filled Organic Salt Compound

We report a novel insulator-insulator transition arising from the internal charge degrees of freedom in the two-dimensional quarter-filled organic salt β-(meso-DMBEDT-TTF)2PF6. The optical conductivity spectra above Tc=70 K display a prominent feature of the dimer Mott insulator, characterized by a substantial growth of a dimer peak near 0.6 eV with decreasing temperature. The dimer peak growth is rapidly quenched as soon as a peak of the charge order appears below Tc, indicating a competition between the two insulating phases. Our infrared imaging spectroscopy has further revealed a spatially competitive electronic phase far below Tc, suggesting a nature of quantum phase transition driven by material-parameter variations.

Proximity of iron pnictide superconductors to a quantum tricritical point.

In several materials, unconventional superconductivity appears nearby a quantum phase transition where long-range magnetic order vanishes as a function of a control parameter like charge doping, pressure or magnetic field. The nature of the quantum phase transition is of key relevance, because continuous transitions are expected to favour superconductivity, due to strong fluctuations. Discontinuous transitions, on the other hand, are not expected to have a similar role. Here we determine the nature of the magnetic quantum phase transition, which occurs as a function of doping, in the iron-based superconductor LaFeAsO1–xFx. We use constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The outcome is intriguing, as this material turns out to be remarkably close to a quantum tricritical point, where the transition changes from continuous to discontinuous, and several susceptibilities diverge simultaneously. We discuss the consequences for superconductivity and the phase diagram.

Diamond chains with multiple-spin exchange interactions

We study the phase diagram of a symmetric spin-1/2 Heisenberg diamond chain with additional cyclic four-spin exchange interactions. The presented analysis supplemented by numerical exact-diagonalization results for finite periodic clusters implies a rich phase diagram containing, apart from standard magnetic and spin-liquid phases, two different tetramer-dimer phases as well as an exotic fourfold degenerate dimerized phase. The characteristics of the established spin phases as well as the nature of quantum phase transitions are discussed as well.

Quantum phase transitions in the shastry-sutherland model for SrCu2(BO3)(2)

We investigate quantum phase transitions in the frustrated antiferromagnetic Heisenberg model for SrCu2(BO3)(2) by using the series expansion method. It is found that a novel spin-gap phase, adiabatically connected to the plaquette-singlet phase, exists between the dimer and the magnetically ordered phases known thus far. When the ratio of the competing exchange couplings alpha( = J'/J) is varied, this spin-gap phase exhibits a first- (second-) order quantum phase transition to the dimer (the magnetically ordered) phase at the critical point alpha(c1) = 0.677(2) [ alpha(c2) = 0. 86(1)]. Our results shed light on some controversial arguments about the nature of quantum phase transitions in this model.