We perform density matrix renormalization group (DMRG) calculations extensively on one-dimensional chains with on site (U) as well as nearest neighbour (V) Coulomb repulsions. The calculations are carried out in full parameter space with explicit inclusion of the static bias and we compare the nature of spin density wave (SDW) and charge density wave (CDW) insulators under the influence of external electric field. We find that, although the SDW (U>2V) and CDW (U<2V) insulators enter into a conducting state after a certain threshold bias, CDW insulators require much higher bias than the SDW insulators for insulator-metal transition at zero temperature. We also find the CDW-SDW phase transition on application of external electric field. The bias required for the transitions in both cases decreases with increase in system size.
The so-called minimal models of unconventional superconductivity are lattice models of interacting electrons derived from materials in which electron pairing arises from purely repulsive interactions. Showing unambiguously that a minimal model actually can have a superconducting ground state remains a challenge at nonperturbative interactions. We make a significant step in this direction by computing ground states of the 2D \mbox{U-V} Hubbard model - the minimal model of the quasi-1D superconductors - by parallelized DMRG, which allows for systematic control of any bias and that is sign-proble…
Using the Kadanoff-Baym-Keldysh formalism, we employ nonequilibrium dynamical mean-field theory to exactly solve for the nonlinear response of an electron-mediated charge-density-wave-ordered material. We examine both the dc current and the order parameter of the conduction electrons as the ordered system is driven by the electric field. Although the formalism we develop applies to all models, for concreteness, we examine the charge-density-wave phase of the Falicov-Kimball model, which displays a number of anomalous behaviors including the appearance of subgap density of states as the tempera…
We investigate the effect of dimensional crossover in the ground state of the antiferromagnetic spin-$1$ Heisenberg model on the anisotropic triangular lattice that interpolates between the regime of weakly coupled Haldane chains ($J^{\prime}\! \!\ll\!\! J$) and the isotropic triangular lattice ($J^{\prime}\!\!=\!\!J$). We use the density-matrix renormalization group (DMRG) and Schwinger boson theory performed at the Gaussian correction level above the saddle-point solution. Our DMRG results show an abrupt transition between decoupled spin chains and the spirally ordered regime at $(J^{\prime}…
We propose a quantum gate architecture that allows for the systematic control of the effective exchange interactions between magnetic impurities embedded in nano-scale graphene flakes connected by a gated bridge. The entanglement between the magnetic moment and the edge states of the fragments is used to electrostatically tune the exchange interaction from ferro to antiferromagnetic by merely changing the bridge's carrier density. By characterizing the effects of size and coupling parameters, we explore different operation regimes of this device by means of exact calculations with the density …
Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful algorithm for finding the ground state in 1D systems, a provably efficient and accurate algorithm remained elusive until the introduction of the rigorous renormalization group (RRG) by Landau et al. [Nature Physics 11, 566 (2015)]. In this paper, we study the accuracy and performance of a numerical implementation of RRG at first order phase transitions and in s…
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent $α$. Using large scale quantum Monte Carlo (QMC) and the density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken Néel phase. We find evidence that the transition is second order.In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- b…
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent $α$. Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken Néel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- boun…
We identify ground states of one-dimensional fermionic systems subject to competing repulsive interactions of finite range, and provide phenomenological and fundamental signatures of these phases and their transitions. Commensurable particle densities admit multiple competing charge-ordered insulating states with various periodicities and internal structure. Our reference point are systems with interaction range $p=2$, where phase transitions between these charge-ordered configurations are known to be mediated by liquid and bond-ordered phases. For increased interaction range $p=4$, we find th…
The anisotropic-exchange spin-1/2 model on a triangular lattice has been used to describe the rare-earth chalcogenides, which may have exotic ground states. We investigate the quantum phase diagram of the model by using the projected entangled pair state (PEPS) method, and compare it to the classical phase diagram. Besides two stripe-ordered phase, and the 120$^\circ$ state, there is also a multi-\textbf{Q} phase. We identify the multi-\textbf{Q} phase as a $Z_{2}$ vortex state. No quantum spin liquid state is found in the phase diagram, contrary to the previous DMRG calculations.
Trirutile-type LiFe$_2$F$_6$ is a charge-ordered material with Fe$^{2+}$/Fe$^{3+}$ configuration. Here its physical properties, including magnetism, electronic structure, phase transition, and charge ordering, are studied theoretically. On one hand, the charge ordering leads to improper ferroelectricity with a large polarization. On the other hand, its magnetic ground state can be tuned from the antiferromagnetic to ferrimagnetic by moderate compressive strain. Thus, LiFe$_2$F$_6$ can be a rare multiferroic with both large magnetization and polarization. Most importantly, since the charge orde…
We numerically study the phase diagram of bosons tightly trapped in the lowest band of an optical lattice and dispersively coupled to a single-mode cavity field. The dynamics is encompassed by an extended Bose-Hubbard model. Here, the cavity-mediated interactions are described by a two-body potential term with a global range and by a correlated tunneling term where the hopping amplitude depends on a global observable. We determine the ground state properties in one dimension by means of the density matrix renormalization group algorithm, focusing on the effects due to the correlated tunneling.…
In this review, we develop the formalism employed to describe charge-density-wave insulators in pump/probe experiments using ultra short driving pulses of light. The theory emphasizes exact results in the simplest model for a charge-density wave insulator (given by a noninteracting systems with two bands and a gap) and by employing nonequilibrium dynamical mean-field theory to solve the Falicov-Kimball model in its ordered phase. We show both how to develop the formalism and how the solutions behave. Care is taken to describe the details behind these calculations and to show how to verify thei…
We investigate a highly frustrated spin-1 model on the triangular lattice, with nearest- and next-nearest-neighbor antiferromagnetic $S\cdot S$ interactions and nearest-neighbor $(S\cdot S)^2$ interactions. Using the density matrix renormalization group (DMRG) technique, we find three magnetically ordered phases, namely 120$^\circ$ spiral order, stripe order, and tetrahedral order, as well as two spin nematic phases: ferroquadrupolar and antiferroquadrupolar. While our data could be consistent with a spin liquid phase between the 120$^\circ$ spiral and antiferroquadrupolar orders, the more lik…
Photoinduced hidden phases are often observed in materials with intertwined orders. Understanding the formation of these non-thermal phases is challenging and requires a resolution of the cooperative interplay between different orders on the ultrashort timescale. In this work, we demonstrate that non-equilibrium photo-excitations can induce a state with spin-orbital orders entirely different from the equilibrium state in the three-quarter-filled two-band Hubbard model. We identify a general mechanism governing the transition to the hidden state, which relies on a non-thermal partial melting of…
The temperature ($T$) - magnetic field ($H$) phase diagram for the tetragonal layered compound CeSbSe, is determined from magnetization, specific heat, and electrical resistivity measurements. This system exhibits complex magnetic ordering at $T_{\rm{M}}$ $=$ 3 K and the application of a magnetic field results in a cascade of magnetically ordered states for $H$ $\lesssim$ 1.8 T which are characterized by fractional integer size steps: i.e., a possible Devil's staircase is observed. Electrical transport measurements show a weak temperature dependence and large residual resistivity which suggest…
The nature of unconventional superconductivity associated with charge density wave order in transition metal dichalcogenides is currently a debated issue. Starting from a normal state elec- tronic structure followed by a charge ordered state how superconductivity in 1T-TiSe 2 arises with applied pressure is still under research. A preformed excitonic liquid driven ordered state mediated superconductivity is found in broad class of TMD on the border of CDW. Using dynamical mean field theory with input from noninteracting band structure calculation, I show a superconducting phase appears near ab…
The phase diagram of the quantum spin-1/2 antiferromagnetic $J^{\,}_{1}$-$J^{\,}_{2}$ XXZ chain was obtained by Haldane using bosonization techniques. It supports three distinct phases for $0\leq J^{\,}_{2}/J^{\,}_{1}<1/2$, i.e., a gapless algebraic spin liquid phase, a gapped long-range ordered Neel phase, and a gapped long-range ordered dimer phase. Even though the Neel and dimer phases are not related hierarchically by a pattern of symmetry breaking, it was shown that they meet along a line of quantum critical points with a U(1) symmetry and central charge $c=1$. Here, we extend the analysi…
The competition of magnetic exchange interactions and tunneling underlies many complex quantum phenomena observed in real materials. We study non-equilibrium magnetization dynamics in an extended 2D system by loading effective spin-1/2 bosons into a spin-dependent optical lattice, and we use the lattice to separately control the resonance conditions for tunneling and superexchange. After preparing a non-equilibrium anti-ferromagnetically ordered state, we observe relaxation dynamics governed by two well-separated rates, which scale with the underlying Hamiltonian parameters associated with sup…
We investigate, by means of a field-theory analysis combined with the density-matrix renormalization group (DMRG) method, a theoretical model for a strongly correlated quantum system in one dimension realizing a topologically-ordered Haldane phase ground state. The model consists of a spin-1/2 Heisenberg chain coupled to a tight-binding chain via two competing Kondo exchange couplings of different type: a "s-wave" Kondo coupling ($J^s_{K}$), and a less common "p-wave" ($J^p_{K}$) Kondo coupling. While the first coupling is the standard Kondo interaction studied in many condensed-matter systems…
We propose a microscopic magneto-electric model in which the coupling between spins and electric dipoles is mediated by lattice distortions. The magnetic sector is described by a spin S=1/2 Heisenberg model coupled directly to the lattice via a standard spin-Peierls term and indirectly to the electric dipole variables via the distortion of the surrounding electronic clouds. Electric dipoles are described by Ising variables for simplicity. We show that the effective magneto-electric coupling which arises due to the interconnecting lattice deformations is quite efficient in one-dimensional array…
Correlation-Driven Orbital-Selective Fermiology and Superconductivity in the Bilayer Nickelate La$_3$Ni$_2$O$_7$
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学与技术重点实验室）
The electrical resistivity of several relatively clean metallic ferromagnets, as well as the helimagnet MnSi, is commonly observed to exhibit non-Fermi-liquid behavior at low temperatures. This behavior, which is found in both ordered and disordered phases, and both near and away from the magnetic transition, remains a major unsolved problem. We derive and discuss three novel mechanisms underlying such behavior that are based on electron scattering mediated by the exchange of (1) ferromagnons or (2) skyrmionic fluctuations, both in conjunction with weak disorder, or (3) helimagnons in clean sy…
Motivated by the recent observation of evidences of ferromagnetism in correlated insulating states in systems with Moiré superlattices, we study a two-orbital quantum antiferromagnetic model on the triangular lattice, where the two orbitals physically correspond to the two valleys of the original graphene sheet. For simplicity this model has a SU(2)$^s$$\otimes$SU(2)$^v$ symmetry, where the two SU(2) symmetries correspond to the rotation within the spin and valley space respectively. Through analytical argument, Schwinger boson analysis and also DMRG simulation, we find that even though all th…
Unraveling the Kagome Antiferromagnetic $3J$ Model and Its Materials: An Integrated Approach
The University of Hong Kong（香港大学）；Univ Toulouse, CNRS, Laboratoire de Physique Théorique（图卢兹大学，法国国家科学研究中心，理论物理实验室）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Emergent QED$_3$ at the bosonic Laughlin state to superfluid transition
University of California, Berkeley（加州大学伯克利分校）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；Hong Kong University of Science and Technology（香港科技大学）；Massachusetts Institute of Technology（麻省理工学院）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S = 1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0 \leq J_2/J_1 \leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 \lesssim 0.27$, the system sustains a Néel antiferromagnetic phase. At the large $J_2$ side $J_2/J_1 \gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phas…
We investigate the non-equilibrium states of an interacting multi-component quantum system when only an extensive subsystem is quantum-quenched or driven from the ground state. As a concrete example, we consider a system where two XXZ spin chains are coupled to a transverse field Ising (TFI) chain, and only the transverse field in the TFI chain is quantum-quenched or periodically driven in time, starting from an initially ordered state. This system is studied using density matrix renormalization group (DMRG) simulations and various entanglement entropy diagnostics. In the case of quantum quenc…
Disordered quantum antiferromagnets in two-dimensional compounds have been a focus of interest in the last years due to their exotic properties. However, with very few exceptions, the ground states of the corresponding Hamiltonians are notoriously difficult to simulate making their characterization and detection very elusive, both, theoretically and experimentally. Here we propose a method to signal quantum disordered antiferromagnets by doing exact diagonalization in small lattices using random boundary conditions and averaging the observables of interest over the different disorder realizati…
