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arXiv:2307.13169 · Physical review. B./Physical review. B

Competing phases and intertwined orders in coupled wires near the self-dual point

Ken K. W., Oğuz Türker, Alexander Seidel, Kun Yang

Published Dec 15, 2023• 2 citations
arXivHTMLPDF

Abstract

The interplay between different quantum phases plays an important role in strongly correlated systems such as high-${T}_{c}$ cuprates, quantum spin systems, and ultracold atoms. In particular, the application of effective-field theory and renormalization group analysis suggests that the coexistence of density wave (DW) and superfluid (SF) orders can lead to a supersolid phase of ultracold bosons. Here we revisit the problem by considering weakly coupled wires, where we treat the intrawire interactions exactly via bosonization and interwire couplings using a mean-field theory which becomes asymptotically exact in the limit of high dimensionality. We obtain and solve the mean-field equations for the system near the self-dual point, where each wire has the Luttinger parameter $K=1$ and the interwire DW and SF coupling strengths are identical. This allows us to find explicit solutions for the possible supersolid order. An energy comparison between different possible solutions shows that the supersolid order is energetically unfavorable at zero temperature. This suggests that the density wave and superfluid phases are connected by a first-order transition near the self-dual point. We also discuss the relation between our work and the intertwining of charge density wave and superconducting orders in cuprates.

DOI
10.1103/physrevb.108.245138

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The interplay between different quantum phases plays an important role in strongly correlated systems such as high-Tc{T}_{c}Tc​ cuprates, quantum spin systems, and ultracold atoms. In particular, the application of effective-field theory and renormalization group analysis suggests that the coexistence of density wave (DW) and superfluid (SF) orders can lead to a supersolid phase of ultracold bosons. Here we revisit the problem by considering weakly coupled wires, where we treat the intrawire interactions exactly via bosonization and interwire couplings using a mean-field theory which becomes asymptotically exact in the limit of high dimensionality. We obtain and solve the mean-field equations for the system near the self-dual point, where each wire has the Luttinger parameter K=1K=1K=1 and the interwire DW and SF coupling strengths are identical. This allows us to find explicit solutions for the possible supersolid order. An energy comparison between different possible solutions shows that the supersolid order is energetically unfavorable at zero temperature. This suggests that the density wave and superfluid phases are connected by a first-order transition near the self-dual point. We also discuss the relation between our work and the intertwining of charge density wave and superconducting orders in cuprates.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
We investigate the interplay between superconductivity and nematic order in a two-dimensional electron gas with competing pairing and quadrupolar forward-scattering interactions. The model includes both sss-wave and ddd-wave superconducting channels. We compute the mean-field free energy density and determine the phase diagrams as functions of interaction strengths and temperature by solving a set of coupled self-consistent equations. At zero-temperature, we find that the nematic order competes strongly with ddd-wave superconductivity, leading to a direct first-order phase transition, while its interplay with sss-wave pairing allows for a coexistence phase characterized by an anisotropic Fermi surface with a uniform superconducting gap. At finite-temperatures, quadrupolar interactions promote the emergence of additional superconducting components, giving rise to regimes where sss-wave, ddd-wave, and nematic orders coexist. Our results highlight the role of symmetry and interaction strength in shaping the phase structure and provide a minimal framework to describe intertwined nematic and superconducting phases in correlated electron systems.
We study a model of strongly-correlated systems that incorporates phases such as Fermi liquids, non-Fermi liquids, and superconductivity, in addition to potential intertwined orders. The model describes Fermi surfaces of spinful electron gas or electron liquid coupled to bosons via an intermediate gauge field. Effectively, the coupling imposes constraints and interactions between the fermion spin and the local boson density. This grants the bosons the meaning as the Schwinger boson of the magnetic order and allows us to probe a larger phase space, rather than around the quantum critical point. We design the initial model so that after the boson and gauge fields are integrated out exactly, the resulting fermion-only effective theory only consists of several local interactions, allowing controlled weak-coupling interpretation for certain parameter regions. Consequently, we find a non-Fermi liquid whose degrees of freedom in the effective theory take the form of an \emph{emergent} Fermi surface that has a different Luttinger volume from the original fermions, therefore explicitly violates the Luttinger theorem. Further, this allows a ddd-wave superconducting instability if the effective interacting induced by boson coupling is in the relevant pairing channel. When the emergent Fermi surface undergoes a Lifshitz transition, the carrier type changes. In addition, we attribute the Mott insulating behavior in the strong coupling limit to the loss of emergent Fermi surface and argue the possibility of coexisting magnetic order. Our effective theory also suggests the possibility of charge density waves as a consequence of \emph{effective} strong repulsion and is independent of the Fermi-surface-nesting scenario. We discuss the possible optimal conditions for higher superconducting transition temperature and potential relevances and implications for realistic materials.
Systems with competing orders are of great interest in condensed matter physics. When\ntwo phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. \n\nIn the first part of the thesis, we study the\n attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis.\n The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments.\n\nWe drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors.\n\nIn the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. \n\nWe then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange.\n For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’\nstates. For S=1/2, this lattice nematic takes the form of a valence bond solid.\n\nWith J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO.\n\nWe discuss implications for the honeycomb lattice Hubbard model.
The supersolid is a long-sought phase in condensed matter physics, characterized by the coexistence of density wave and superfluid orders. This phase is counterintuitive, as different symmetry-breaking orders typically compete with one another. A deeper understanding of how such a state forms in condensed matter systems remains an open question, especially in quasi-one-dimensional correlated systems. In this work, we investigate the emergence of supersolids in Luttinger-Emery liquids using a variational method. As the system consists of coupled Luttinger-Emery liquid chains, we refer to this phase as a quasi-one-dimensional supersolid. Notably, we demonstrate that the quasi-one-dimensional supersolid phase is energetically favorable in chains with finite size or short-range order. Furthermore, we investigate the collective dynamics of these coexisting charge density waves and superconducting states, identifying a quasi-Goldstone mode. Our theory provides valuable insights into both the ground state and the dynamic properties of supersolids in strongly correlated systems.
We investigate the properties of strongly interacting bosons in two dimensions at zero temperature using mean-field theory, a variational ansatz for the ground-state wave function, and Monte Carlo methods. With on-site and short-range interactions a rich phase diagram is obtained. Apart from the homogeneous superfluid and Mott-insulating phases, inhomogeneous charge-density wave phases appear, that are stabilized by the finite-range interaction. Furthermore, our analysis demonstrates the existence of a supersolid phase, in which both long-range order (related to the charge-density wave) and off-diagonal long-range order coexist. We also obtain the critical exponents for the various phase transitions.