Featured Researches

Strongly Correlated Electrons

A Z 3 quantum double in a superconducting wire array

We show that a Z 3 quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the inter-wire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry -- a local Z 3 symmetry involving permutations and shifts by ±2?/3 of the superconducting phases. The sign of the star potential resulting from the Josephson energy is inverted in this physical realization, leading to a massive degeneracy in the non-zero flux sectors. A dimerization pattern encoded in the capacitances of the array lifts up these degeneracies, resulting in a Z 3 topologically ordered state. Moreover, this dimerization pattern leads to a larger effective vison gap as compared to the canonical case with the usual (uninverted) star term. We further show that our model maps to a quantum three-state Potts model under a duality transformation. We argue, using a combination of bosonization and mean field theory, that altering the dimerization pattern of the capacitances leads to a transition from the Z 3 topological phase into a quantum XY-ordered phase. Our work highlights that combinatorial gauge symmetry can serve as a design principle to build quantum double models using systems with realistic interactions.

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Strongly Correlated Electrons

A Colossal Electroresistance response, accompanied by metal-insulator transition, in a mixed-valent vanadate

Colossal electroresistance (CER) in manganites, i.e., a large change in electrical resistance under the influence of either an applied electric field or an applied electric current, has often been described as complimentary to the colossal magnetoresistance (CMR) effect. Mixed valent vanadates with active t2g and empty eg orbitals, unlike manganites, have not naturally been discussed in this context, as double exchange based CMR is not realizable in them. However, presence of coupled spin and orbital degrees of freedom, metal-insulator transition (MIT) accompanied by orbital order-disorder transition, etc., anyway make the vanadates an exciting group of materials. Here we probe a Fe-doped hollandite lead vanadate PbFe1.75V4.25O11 (PFVO), which exhibits a clear MIT as a function of temperature. Most importantly, a giant fall in the resistivity, indicative of a CER, as well as a systematic shift in the MIT towards higher temperature are observed as a function of applied electric current. Detailed structural, magnetic, thermodynamic and transport studies point towards a complex interplay between orbital order/disorder effect, MIT and double exchange in this system.

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Strongly Correlated Electrons

A Commuting Projector Model with a Non-zero Quantized Hall conductance

By ungauging a recently discovered lattice rotor model for Chern-Simons theory, we create an exactly soluble path integral on spacetime lattice for U κ (1) Symmetry Protected Topological (SPT) phases in 2+1 dimensions with a non-zero Hall conductance. We then convert the path integral on a 2+1 d spacetime lattice into a 2 d Hamiltonian lattice model, and show that the Hamiltonian consists of mutually commuting local projectors. We confirm the non-zero Hall conductance by calculating the Chern number of the exact ground state. It has recently been suggested that no commuting projector model can host a nonzero Hall conductance. We evade this no-go theorem by considering a rotor model, with a countably infinite number of states per site.

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Strongly Correlated Electrons

A Contemporary Model Description of Magnetism

A treatment of many-electron polar and s?�d(f) exchange models is carried out in connection with the development of the theory of magnetism of transition and rare-earth metals, as well as their compounds. Particular emphasis is placed on the derivation of the many-electron Heisenberg, Hubbard, Anderson and t?�J models, as well as the internal relationship between them. Among the topics discussed are many-electron approaches in describing systems of d - and f -electrons, atomic representation of Hubbard's X -operators, slave-particle representations, the problem of strong itinerant magnetism and the formation of local moments, the role of non-quasiparticle (incoherent states). The application of these concepts to strongly correlated systems, in particular, to half-metallic ferromagnets and Kondo lattices, is discussed. A comparison is performed with modern field-theoretical and topological approaches.

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Strongly Correlated Electrons

A Subsystem Ginzburg-Landau and SPT Orders Co-existing on a Graph

We analyze a model demonstrating the co-existence of subsystem symmetry breaking (SSB) and symmetry-protected topological (SPT) order, or subsystem LSPT order for short. Its mathematical origin is the existence of both a subsystem and a local operator, both of which commute with the Hamiltonian but anti-commute between themselves. The reason for the exponential growth of the ground state degeneracy is attributed to the existence of subsystem symmetries, which allows one to define both the Landau order parameter and the SPT-like order for each independent loop.

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Strongly Correlated Electrons

A catastrophic charge density wave in BaFe 2 Al 9

Charge density waves (CDW) are modulations of the electron density and the atomic lattice that develop in some crystalline materials at low temperature. We report an unusual example of a CDW in BaFe 2 Al 9 below 100 K. In contrast to the canonical CDW phase transition, temperature dependent physical properties of single crystals reveal a first-order phase transition. This is accompanied by a discontinuous change in the size of the crystal lattice. In fact, this large strain has catastrophic consequences for the crystals causing them to physically shatter. Single crystal x-ray diffraction reveals super-lattice peaks in the low-temperature phase signaling the development of a CDW lattice modulation. No similar low-temperature transitions are observed in BaCo 2 Al 9 . Electronic structure calculations provide one hint to the different behavior of these two compounds; the d-orbital states in the Fe compound are not completely filled. Iron compounds are renowned for their magnetism and partly filled d-states play a key role. It is therefore surprising that BaFe 2 Al 9 develops a structural modulation instead at low temperature instead of magnetic order.

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Strongly Correlated Electrons

A cluster-based mean-field, perturbative and coupled-cluster theory description of strongly correlated systems

We introduce cluster-based mean-field, perturbation and coupled-cluster theories to describe the ground state of strongly-correlated spin systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product of optimized cluster states. The cluster-language and the mean-field nature of the ansatz allows for a straightforward improvement based on perturbation theory and coupled-cluster, to account for inter-cluster correlations. We present benchmark calculations on the 2D square J 1 ??J 2 Heisenberg model, using cluster mean-field, second-order perturbation theory and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies very accurately. Our results indicate that, even with relatively small clusters, the correlated methods can provide an accurate description of the Heisenberg model in the regimes considered. Some ways to improve the results presented in this work are discussed.

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Strongly Correlated Electrons

A continuous metal-insulator transition driven by spin correlations

Metal-insulator transitions involve a mix of charge, spin, and structural degrees of freedom, and when strongly-correlated, can underlay the emergence of exotic quantum states. Mott insulators induced by the opening of a Coulomb gap are an important and well-recognized class of transitions, but insulators purely driven by spin correlations are much less common, as the reduced energy scale often invites competition from other degrees of freedom. Here we demonstrate a clean example of a spin-correlation-driven metal-insulator transition in the all-in-all-out pyrochlore antiferromagnet Cd2Os2O7, where the lattice symmetry is fully preserved by the antiferromagnetism. After the antisymmetric linear magnetoresistance from conductive, ferromagnetic domain walls is carefully removed experimentally, the Hall coefficient of the bulk reveals four Fermi surfaces, two of electron type and two of hole type, sequentially departing the Fermi level with decreasing temperature below the Néel temperature, T_N. Contrary to the common belief of concurrent magnetic and metal-insulator transitions in Cd2Os2O7, the charge gap of a continuous metal-insulator transition opens only at T~10K, well below T_N=227K. The insulating mechanism resolved by the Hall coefficient parallels the Slater picture, but without a folded Brillouin zone, and contrasts sharply with the behavior of Mott insulators and spin density waves, where the electronic gap opens above and at T_N, respectively.

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Strongly Correlated Electrons

A full configuration interaction quantum Monte Carlo study of ScO, TiO and VO molecules

Accurate ab initio calculations of 3d transition metal monoxide molecules have attracted extensive attention because of its relevance in physical and chemical science, as well as theoretical challenges in treating strong electron correlation. Meanwhile, recent years have witnessed the rapid development of full configuration interaction quantum Monte Carlo (FCIQMC) method to tackle electron correlation. In this study, we carry out FCIQMC simulations to ScO, TiO and VO molecules and obtain accurate descriptions of 13 low-lying electronic states (ScO 2 Σ + , 2 ? , 2 ? ; TiO 3 ? , 1 ? , 1 Σ + , 3 ? , 3 Φ ; VO 4 Σ ??, 4 Φ , 4 ? , 2 ? , 2 ? ), including states that have significant multi-configurational character. The FCIQMC results are used to assess the performance of several other wave function theory and density functional theory methods. Our study highlights the challenging nature of electronic structure of transition metal oxides and demonstrates FCIQMC as a promising technique going forward to treat more complex transition metal oxide molecules and materials.

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Strongly Correlated Electrons

A microscopic derivation of the Dirac composite fermion theory: aspects of non-commutativity and pairing instabilities

Building on previous work [1 and 2] on the system of bosons at filling factor ν=1 we derive the Dirac composite fermion theory for a half-filled Landau level from first principles and applying Hartree-Fock approach in a preferred representation. On the basis of the microscopic formulation, in the long-wavelength limit, we propose a non-commutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. The microscopic representation of the problem is also used to discuss pairing instabilities of composite fermions. We find that a presence of a particle-hole symmetry breaking leads to a weak (BCS) coupling p -wave pairing in the lowest Landau level, and strong coupling p -wave pairing in the second Landau level that occurs in a band with nearly flat dispersion - a third power function of momentum.

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