A class of Aubry-André-Harper models of spin-orbit coupled electrons exhibits a topological phase diagram where two regions belonging to the same phase are split up by a multicritical point. The critical lines which meet at this point each defines a topological quantum phase transition with a second-order nonanalyticity of the ground-state energy, accompanied by a linear closing of the spectral gap with respect to the control parameter; except at the multicritical point which supports fourth-order transitions with parabolic gap-closing. Here both types of criticality are characterized through a scaling analysis of the curvature function defined from the topological invariant of the model. We extract the critical exponents of the diverging curvature function at the non-high symmetry points in the Brillouin zone where the gap closes, and also apply a renormalization group approach to the flattening curvature function at high symmetry points. We also derive a basis-independent correlation function between Wannier states to characterize the transition. Intriguingly, we find that the critical exponents and scaling law defined with respect to the spectral gap remain the same regardless of the order of the transition.
A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in the ground-state energy in the thermodynamic limit implies a QPT. Here we report on a finding that challenges this assertion. As a case study we take a phase diagram of a one-dimensional band insulator with spin-orbit coupled electrons, supporting trivial and topological gapped phases separated by intersecting critical surfaces. The intersections define multicritical lines across which the ground-state energy becomes nonanalytical, concurrent with a closing of the band gap, but with no phase transitio…
We investigate multicritical phenomena in O(N)+O(M)-models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications f…
We theoretically explore the mechanism of the colossal magnetoresistance in manganese oxides by explicitly taking into account the phase competition between the double-exchange ferromagnetism and the charge-ordered insulator. We find that quenched disorder causes a drastic change of the multicritical phase diagram by destroying the charge-ordered state selectively. As a result, there appears a nontrivial phenomenon of the disorder-induced insulator-to-metal transition in the multicritical regime. On the contrary, the disorder induces a highly-insulating state above the transition temperature w…
We study the multicritical behavior for the semimetal-insulator transitions on graphene's honeycomb lattice using the Gross-Neveu-Yukawa effective theory with two order parameters: the SO(3) (Heisenberg) order parameter describes the antiferromagnetic transition, and the $\mathbb{Z}_2$ (Ising) order parameter describes the transition to a staggered density state. Their coupling induces multicritical behavior which determines the structure of the phase diagram close to the multicritical point. Depending on the number of fermion flavors $N_f$ and working in the perturbative regime in vicinity of…
We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal (DSM) and a symmetry-preserving band insulator (BI). The electronic dispersion at this critical point is anisotropic ($E_{\mathbf k}=\pm \sqrt{v^2 k^2_x + b^2 k^{2n}_y}$ with $n=2$), which results in unconventional scaling of physical observables. Due to the vanishing density of states ($\varrho(E) \sim |E|^{1/n}$), this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions t…
We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. This analysis reveals an intricate flow with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The slow flow along this special line has significant consequences on the physics of the mul…
The colossal magnetoresistance in manganites AMnO_3 is studied from the viewpoint of multicritical phenomena. To understand the complicated interplay of various phases, we study the Ginzburg-Landau theory in terms of both the mean-field approximation and the renormalization-group analysis to compare with the observed phase diagram. Several novel features, such as the first-order ferromagnetic transition, and the dip in the transition temperature near the multicritical point, can be understood as driven by enhanced fluctuations near the multicritical point. Furthermore, we obtain a universal sc…
We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, th…
Boundary Criticality at the Nishimori Multicritical Point
Institute for Advanced Study in Physics and School of Physics, Zhejiang University（浙江大学物理学院与高等研究院）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram of this model is constructed in terms of the disorder strength and the chemical potential. Via quantum Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where a random potential is irrelevant, from the strong-disorder regime. In the weak-disorder regime, the Mott-insulator-to-superfluid transition occurs, while, in the strong-disorder regime, the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-supe…
Topological order in solid state systems is often calculated from the integration of an appropriate curvature function over the entire Brillouin zone. At topological phase transitions where the single particle spectral gap closes, the curvature function diverges and changes sign at certain high symmetry points in the Brillouin zone. These generic properties suggest the introduction of a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We apply this scheme to a variety of interacting topological insulators in different dimension…
From QED$_3$ to Self-Dual Multicriticality in the Fradkin-Shenker Model
Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校曼尼·L·巴乌米克理论物理研究所）；SISSA（的里雅斯特国际高等研究学院）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
The effect of quenched disorder on the multiphase competition has been investigated by examining the pressure phase diagram of half doped manganite Ln0.5B0.5MnO3 (Ln = Sm and Nd) with A-site disorders. Sm0.5Ba0.5MnO3, a spin glass insulator at ambient pressure, switches to a ferromagnetic metal with increasing pressure, followed by a rapid increase of the ferromagnetic transition temperature Tc. The rapid increase of Tc was confirmed also for Nd0.5Ba0.5MnO3. These observations indicate that the unusual suppression of the multicritical phase boundary in the A-site disordered system, previously …
We explore the scaling description for a two-dimensional metal-insulator transition (MIT) of electrons in silicon. Near the MIT, $β_{T}/p = (-1/p)d(\ln g)/d(\ln T)$ is universal (with $p$, a sample dependent exponent, determined separately; $g$--conductance, $T$--temperature). We obtain the characteristic temperatures $T_0$ and $T_1$ demarking respectively the quantum critical region and the regime of validity of single parameter scaling in the metallic phase, and show that $T_1$ vanishes as the transition is approached. For $T<T_1$, the scaling of the data requires a second parameter. Moreove…
Using uniaxial stress to tune Si:B through the metal-insulator transition we find the conductivity at low temperatures shows an excellent fit to scaling with temperature and stress on both sides of the transition. The scaling functions yield the conductivity in the metallic and insulating phases, and allow a reliable determination of the temperature dependence in the critical regions on both sides of the transition.
We report a detailed scaling analysis of resistivity ρ(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the ρ(T,n) data.
We present a scaling description of a metal-insulator transition in two-dimensional electron systems that is driven by a vanishing compressibility rather than a vanishing diffusion coefficient. A small set of basic assumptions leads to a consistent theoretical framework that is compatible with existing transport and compressibility measurements, and allows to make predictions for other observables. We also discuss connections between these ideas and other theories of transitions to an incompressible quantum fluid.
The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of disordered $\mathbb{Z}_2$ topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel s…
The established scaling laws of the conductivity with temperature and doping are strong indications for the quantum nature of the metal-insulator transition in YH$_x$. Here we report the first results on the frequency scaling of the conductivity. Samples were brought from the insulating to the metallic phase by carrier doping via illumination. In the metallic phase, the sub-terahertz conductivity coincides with the dc data. These results do not agree with the simplest picture of a quantum-phase transition.
By applying a multi-stage real-space renormalization group procedure to Hubbard model, we examine the finite-size scaling in Mott metal-insulator transition(MIT) on a non-partite lattice. It is found that there exists a critic point U/t=12.5 for the MIT and the corresponding critical exponent for correlation length niu= 1 and the dynamic exponent z = 0.91 are obtained. On the critical point, the charge gap scales with the system size as Delta-g~1/L^0.91.
We note that data on Si/SiGe heterostructures, reported in the Comment of Ismail et al. (cond-mat/9707061) on our recent Letter (cond-mat/9608101), are insufficient to establish the claim for a transition to a metallic phase.
We discuss the recently discovered two-dimensional metal-insulator transition in zero magnetic field in the light of the scaling theory of localization. We demonstrate that the observed symmetry relating conductivity and resistivity follows directly from the quantum critical behavior associated with such a transition. In addition, we show that very general scaling considerations imply that any disordered two dimensional metal is a perfect metal, but most likely not a Fermi liquid.
The spin-1/2 transverse field two-leg Ising ladder with nearest-neighbor exchange and plaquette four-spin interaction $J_{4}$ is studied analytically and numerically with the density matrix renormalization group approach. The quantum phase diagram in the transverse field $B$ versus $J_{4}$ plane has been obtained. There are three different phases: a paramagnetic (PM) phase for high values of the transverse field and, for low values of $B$, a ferromagnetic (FM) ordered phase for small $J_{4}$ and a dimerized-rung (DR) phase for large negative values of $J_{4}$. All phases are separated by quant…
We study ground state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe in detail cases when fidelity is dominated by the universal contribution reflecting quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting…
We consider the Ising phase of the antiferromagnetic XXZ Heisenberg chain on a finite-size lattice with N sites.We compute the large $N$ behavior of the spin stiffness, obtaining the correlation length ξ. We use our results to discuss the scaling behavior of metal-insulator transitions in 1D systems, taking into account the mapping between the XXZ Heisenberg chain and the spinless fermion model and known results for the Hubbard model. We study the scaling properties of both the Hubbard model and the XXZ Heisenberg chain, by solving numerically the Bethe Ansatz equations. We find that for some …
The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from w_k-scaling of the conductivity towards w_k/T-scaling at low Matsubara frequencies w_k. By careful analytic continuation using Pade approximants we show that this behavior carries over to the real frequency axis where the conductivity scales wit…
We consider a two-component scaling picture for the resistivity of two-dimensional (2D) weakly disordered interacting electron systems at low temperature with the aim of describing both the vicinity of the bifurcation and the low resistance metallic regime in the same framework. We contrast the essential features of one-component and two-component scaling theories. We discuss why the conventional lowest order renormalization group equations do not show a bifurcation in 2D, and a semi-empirical extension is proposed which does lead to bifurcation. Parameters, including the product $zν$, are det…
For an electron density near the H=0 insulator-to-conductor transition, the magnetoconductivity of the low-temperature conducting phase in high-mobility silicon MOSFETs is consistent with the form $Δσ(H_{||},T)\equivσ(H_{||},T)-σ(0,T) = f(H_{||}/T)$ for magnetic fields $H_{||}$ applied parallel to the plane of the electron system. This sets a valuable constraint on theory and provides further evidence that the electron spin is central to the anomalous H=0 conducting phase in two dimensions.
Electron-electron scattering usually dominates the transport in strongly correlated materials. It typically leads to pronounced resistivity maxima in the incoherent regime around the coherence temperature $T^{*}$, reflecting the tendency of carriers to undergo Mott localization following the demise of the Fermi liquid. This behavior is best pronounced in the vicinity of interaction-driven (Mott-like) metal-insulator transitions, where the $T^{*}$ decreases, while the resistivity maximum $ρ_{max}$ increases. Here we show that, in this regime, the entire family of resistivity curves displays a c…
Metal-insulator transitions driven by magnetic fields have been extensively studied in 2D, but a 3D theory is still lacking. Motivated by recent experiments, we develop a scaling theory for the metal-insulator transitions in the strong-magnetic-field quantum limit of a 3D system. By using a renormalization-group calculation to treat electron-electron interactions, electron-phonon interactions, and disorder on the same footing, we obtain the critical exponent that characterizes the scaling relations of the resistivity to temperature and magnetic field. By comparing the critical exponent with th…
Magnetic field and temperature dependence of the Terahertz conductivity and permittivity of the colossal magnetoresistance manganite Pr_{0.65}Ca_{0.28}Sr_{0.07}MnO_3 (PCSMO) is investigated approaching the metal-to-insulator transition (MIT) from the insulating side. In the charge-ordered state of PCSMO both conductivity and dielectric permittivity increase as function of magnetic field and temperature. Universal scaling relationships between the changes in permittivity and conductivity are observed in a broad range of temperatures and magnetic fields. Similar scaling is also seen in La_{1-x}S…
Electron tunneling experiments are used to probe Coulomb correlation effects in the single-particle density-of-states (DOS) of boron-doped silicon crystals near the critical density of the metal-insulator transition (MIT). At low energies, a DOS measurement distinguishes between insulating and metallic samples with densities 10 to 15 % on either side of the MIT. However, at higher energies the DOS of both insulators and metals show a common behavior, increasing roughly as the square-root of energy. The observed characteristics of the DOS can be understood using a classical treatment of Coulomb…
In a recent Letter, Kravchenko et al. [cond-mat/9608101] have provided evidence for a metal-insulator transition (MIT) in a two-dimensional electron system (2DES) in Si metal-oxide-semiconductor field-effect transistors (MOSFETs). The transition observed in these samples occurs at relatively low electron densities $n_{s}\sim (1-2)\times 10^{11}cm^{-2}$ and high disorder $σ_{c}\sim e^{2}/2h$. We present evidence for a 2D MIT in a structure where the disorderis about two orders of magnitude weaker than in Si MOSFETs. The MIT occurs in the same range of $n_s$ Providing very strong evidence that t…
The possibility of the strong electron-electron interaction driven insulating phase from the metallic phase in two-dimensions has been suggested for clean systems without intentional disorder, but its rigorous demonstration is still lacking. Here, we examine the finite-temperature transport behavior of a few layered-MoS$_2$ material in the vicinity of the density-driven metal-insulator transition (MIT), revealing previously overlooked universal features characteristic of strongly correlated electron systems. Our scaling analysis, based on the Wigner-Mott theoretical viewpoint, conclusively dem…
We have varied the disorder in a two-dimensional electron system in silicon by applying substrate bias. When the disorder becomes sufficiently low, we observe the emergence of the metallic phase, and find evidence for a metal-insulator transition (MIT): the single-parameter scaling of conductivity with temperature near a critical electron density. We obtain the scaling function $β$, which determines the length (or temperature) dependence of the conductance. $β$ is smooth and monotonic, and linear in the logarithm of the conductance near the MIT, in agreement with the scaling theory for interac…
We investigate the neutral-to-ionic insulator-insulator transition in one-dimensional materials by treating a strong-coupling effective model based on the ionic Hubbard model using the density-matrix renormalization group and finite-size scaling. The effective model, formulated in a spin-one representation, contains a single parameter. We carry out an extensive finite-size scaling analysis of the relevant gaps and susceptibilities to characterize the two zero-temperature transitions. We find that the transition from the ionic band-insulating phase to an intermediate spontaneously dimerized pha…
Millimeter-wave transmission measurements have been performed in amorphous niobium-silicon alloy samples where the DC conductivity follows the critical temperature dependence $σ_{dc} \propto T^{1/2}$. The real part of the conductivity is obtained at eight frequencies in the range 87--1040 GHz for temperatures 2.6 K and above. In the quantum regime ($\hbar ω> k_B T$) the real part of the high-frequency conductivity has a power-law frequency dependence $Re~σ(ω) \propto ω^{1/2}$. For temperatures 16 K and below the data exhibits temperature-frequency scaling predicted by theories of dynamics near…
Finding microscopic models for metallic states that exhibit quantum critical properties such as $ω/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $χ(T,ω)$ for a Hubbard model at half filling using Dynamical Mean-Field Theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite temperature critical point. The signature of the latter is $ω/T$ scaling where $T$ is the temperature.…
We investigate the interaction-induced superfluid-to-Mott insulator transition in the one-dimensional Bose-Hubbard model (BHM) for fillings $n=1$, $n=2$, and $n=3$ by studying the single-particle gap, the fidelity susceptibility, and the amplitude of Bloch oscillations via density-matrix renormalization-group methods. We apply a generic scaling procedure for the gap, which allows us to determine the critical points with very high accuracy. We also study how the fidelity susceptibility behaves across the phase transition. Furthermore, we show that in the BHM, and in a system of spinless fermion…
We report on the temperature and field driven metal-insulator transition in disordered Ge:Mn magnetic semiconductors accompanied by magnetic ordering, magnetoresistance reaching thousands of percents and suppression of the extraordinary Hall effect by a magnetic field. Magnetoresistance isotherms are shown to obey a universal scaling law with a single scaling parameter depending on temperature and fabrication. We argue that the strong magnetic disorder leads to localization of charge carriers and is the origin of the unusual properties of Ge:Mn alloys.
We discuss a metal-insulator transition caused by random couplings of magnetic moments in itinerant systems. An analytic solution for the single particle Green function is derived from dynamical self consistency equations, the corresponding density of states is characterized by the opening of a gap. The scaling behavior of observables is analyzed in the framework of a scaling theory and different crossover lines are identified. A fluctuation expansion around the mean field solution accounts for both interaction and localization effects in a consistent manner and is argued to be relevant for th…
We study the phase diagram and the quantum phase transitions of a site-diluted two-dimensional O(3) quantum rotor model by means of large-scale Monte-Carlo simulations. This system has two quantum phase transitions, a generic one for small dilutions, and a percolation transition across the lattice percolation threshold. We determine the critical behavior for both transitions and for the multicritical point that separates them. In contrast to the exotic scaling scenarios found in other random quantum systems, all these transitions are characterized by finite-disorder fixed points with power-law…
Systems near to quantum critical points show universal scaling in their response functions. We consider whether this scaling is reflected in their fluctuations; namely in current-noise. Naive scaling predicts low-temperature Johnson noise crossing over to noise power $\propto E^{z/(z+1)}$ at strong electric fields. We study this crossover in the metallic state at the 2d z=1 superconductor/insulator quantum critical point. Using a Boltzmann-Langevin approach within a 1/N-expansion, we show that the current noise obeys a scaling form $S_j=T Φ[T/T_{eff}(E)]$ with $T_{eff} \propto \sqrt{E}$. We re…
We study transport in a one-dimensional boundary-driven Anderson insulator (the XX spin chain with onsite disorder) with randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a critical density of sites with dephasing. This model is intended to mimic the passage of an excitation through (many-body) insulating regions or ergodic bubbles, therefore providing a toy model for the diffusion-subdiffusion transition observed in the disordered Heisenberg model [1]. We also present the exact solution of a semiclassical model of conductors and i…
Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal scaling curve. For large values of the argument, the scaling function is well fit by the exponentially activated form associated with variable range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence …
Two phenomena have been recently observed in high-mobility Si MOS structures: (1) strong enhancement of the metallic conduction at low temperatures, T < 2K, and (2) the scaling behavior of the temperature and electric field dependences of the resistivity. These results evidence for the true metal-insulator transition in 2d, in apparent disagreement with the one-parameter scaling theory. Here we present a model that explains both effects in the framework of the spin-orbit interaction and provides a quantitative agreement with the experimental data.
The electrical transport properties of ultrathin YBCO films have been modified using an electric double layer transistor configuration employing an ionic liquid. The films were grown on SrTiO3 substrates using high pressure oxygen sputtering. A clear evolution from superconductor to insulator was observed in nominally 7 unit cell thick films. Using a finite size scaling analysis, curves of resistance versus temperature, R(T), over the temperature range from 6K to 22K were found to collapse onto a single scaling function, which suggests the the presence of a quantum critical point. However the …
In contrast to the Landau paradigm, a metal-insulator transition (MIT), driven purely by competition between itinerance and localization and unaccompanied by any conventional (e.g, magnetic) order-disorder instabilities, admits no obvious local order parameter. Here, we present a detailed analysis of the quantum criticality in magneto-transport data on the alloy Nb$_{1-x}$Ti$_{x}$N across a Ti-doping-driven a MIT. We demonstrate, for the first time, clear and novel quantum criticality reflected in the full conductivity tensor across the MIT. Wide ranging, comprehensive accord with recent theor…
It is shown that the Anderson-Mott metal-insulator transition of paramagnetic, interacting disordered electrons in an external magnetic field is in the same universality class as the transition from a ferromagnetic metal to a ferromagnetic insulator discussed recently. As a consequence, large corrections to scaling exist in the magnetic-field universality class, which have been neglected in previous theoretical descriptions. The nature and consequences of these corrections to scaling are discussed.
Even though no local order parameter in the sense of the Landau theory exists for topological quantum phase transitions in Chern insulators, the highly non-local Berry curvature exhibits critical behavior near a quantum critical point. We investigate the critical properties of its real space analog, the local Chern marker, in weakly disordered Chern insulators. Due to disorder, inhomogeneities appear in the spatial distribution of the local Chern marker. Their size exhibits power-law scaling with the critical exponent matching the one extracted from the Berry curvature of a clean system. We dr…
