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Physical review. B./Physical review. B

Bose metal in an exactly solvable model with infinite-range Hatsugai-Kohmoto interaction

Wei-Wei Yang, Hong‐Gang Luo, Yin Zhong

Published Dec 14, 2023• 8 citations
Publisher

Abstract

In a conventional boson system, the ground state can either be an insulator or a superfluid (SF) due to the duality between particle number and phase. This paper reveals that the long-sought Bose metal (BM) state can be realized in an exactly solvable interacting bosonic model, i.e., the Bose-Hatsugai-Kohmoto (BHK) model, which acts as the nontrivial extension of Bose-Hubbard (BH) model. By tuning the parameters such as bandwidth $W$, chemical potential $\ensuremath{\mu}$, and interaction strength $U$, a BM state without any symmetry breaking can be accessed for a generic $W/U$ ratio, while a Mott insulator (MI) with integer boson density is observed at small $W/U$. The quantum phase transition between the MI and BM states belongs to the universality class of the Lifshitz transition, which is further confirmed by analyzing the momentum-distribution function, the Drude weight, and the SF weight. Additionally, our investigation at finite temperature reveals similarities between the BM state and the Fermi liquid, such as a linear-$T$ dependent heat capacity ($Cv\ensuremath{\sim}\ensuremath{\gamma}T$) and a saturated charge susceptibility (${\ensuremath{\chi}}_{c}\ensuremath{\sim}$ constant) as $T$ approaches zero. Comparing the BM state with the SF state in the standard BH model, we find that the key feature of the BM state is a compressible total wavefunction accompanied by an incompressible zero-momentum component. Given that the BM state prevails over the SF state at any finite $U$ in the BHK model, our paper suggests the possibility of realizing the BM state with on-site repulsion interactions in momentum space.

DOI
10.1103/physrevb.108.235149

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In a conventional boson system, the ground state can either be an insulator or a superfluid (SF) due to the duality between particle number and phase. This paper reveals that the long-sought Bose metal (BM) state can be realized in an exactly solvable interacting bosonic model, i.e., the Bose-Hatsugai-Kohmoto (BHK) model, which acts as the nontrivial extension of Bose-Hubbard (BH) model. By tuning the parameters such as bandwidth WWW, chemical potential \ensuremathμ\ensuremath{\mu}\ensuremathμ, and interaction strength UUU, a BM state without any symmetry breaking can be accessed for a generic W/UW/UW/U ratio, while a Mott insulator (MI) with integer boson density is observed at small W/UW/UW/U. The quantum phase transition between the MI and BM states belongs to the universality class of the Lifshitz transition, which is further confirmed by analyzing the momentum-distribution function, the Drude weight, and the SF weight. Additionally, our investigation at finite temperature reveals similarities between the BM state and the Fermi liquid, such as a linear-TTT dependent heat capacity (Cv\ensuremath∼\ensuremathγTCv\ensuremath{\sim}\ensuremath{\gamma}TCv\ensuremath∼\ensuremathγT) and a saturated charge susceptibility (\ensuremathχc\ensuremath∼{\ensuremath{\chi}}_{c}\ensuremath{\sim}\ensuremathχc​\ensuremath∼ constant) as TTT approaches zero. Comparing the BM state with the SF state in the standard BH model, we find that the key feature of the BM state is a compressible total wavefunction accompanied by an incompressible zero-momentum component. Given that the BM state prevails over the SF state at any finite UUU in the BHK model, our paper suggests the possibility of realizing the BM state with on-site repulsion interactions in momentum space.
In a conventional boson system, the ground state can either be an insulator or a superfluid (SF) due to the duality between particle number and phase. This paper reveals that the long-sought Bose metal (BM) state can be realized in an exactly solvable interacting bosonic model, i.e. the Bose-Hatsugai-Kohmoto (BHK) model, which acts as the nontrivial extension of Bose-Hubbard (BH) model. By tuning the parameters such as bandwidth WWW, chemical potential μμμ, and interaction strength UUU, a BM state without any symmetry-breaking can be accessed for a generic W/UW/UW/U ratio, while a Mott insulator (MI) with integer boson density is observed at small W/UW/UW/U. The quantum phase transition between the MI and BM states belongs to the universality class of the Lifshitz transition, which is further confirmed by analyzing the momentum-distribution function, the Drude weight, and the superfluid density. Additionally, our investigation at finite temperature reveals similarities between the BM state and the Fermi liquid, such as a linear-TTT dependent heat capacity (Cv∼γTCv\sim γTCv∼γT) and a saturated charge susceptibility ($χ_{c} \sim $ constant) as TTT approaches zero. Comparing the BM state with the SF state in the standard BH model, we find that the key feature of the BM state is a compressible total wavefunction accompanied by an incompressible zero-momentum component. Given that the BM state prevails over the SF state at any finite UUU in the BHK model, our work suggests the possibility of realizing the BM state with on-site repulsion interactions in momentum space.
Computing superconducting properties starting from an exactly solvable model for a doped Mott insulator stands as a grand challenge. We have recently shown that this can be done starting from the Hatsugai-Kohmoto (HK) model, which can be understood generally as the minimal model that breaks the nonlocal Z2{\mathbb{Z}}_{2}Z2​ symmetry of a Fermi liquid, thereby constituting a new quartic fixed point for Mott physics [Phillips et al., Nat. Phys. 16, 1175 (2020); Huang et al., Nat. Phys. (2022)]. In the current paper, we compute the thermodynamics, condensation energy, and electronic properties such as the NMR relaxation rate 1/T11/{T}_{1}1/T1​ and ultrasonic attenuation rate. Key differences arise with the standard BCS analysis from a Fermi liquid: (1) the free energy exhibits a local minimum at Tp{T}_{p}Tp​ where the pairing gap turns on discontinuously above a critical value of the repulsive HK interaction, thereby indicating a first-order transition; (2) a tricritical point emerges, thereby demarcating the boundary between the standard second-order superconducting transition and the novel first-order regime; (3) Mottness changes the sign of the quartic coefficient in the Landau-Ginzburg free-energy functional relative to that in BCS; (4) as this obtains in the strongly interacting regime, it is Mott physics that underlies the generic first-order transition; (5) the condensation energy exceeds that in BCS theory suggesting that multiple Mott bands might be a way of enhancing superconducting; (6) the heat-capacity jump is nonuniversal and increases with the Mott scale; (7) Mottness destroys the Hebel-Slichter peak in NMR; and (8) Mottness enhances the fall-off of the ultrasonic attenuation at the pairing temperature Tp{T}_{p}Tp​. As several of these properties are observed in the cuprates, our analysis here points a way forward in computing superconducting properties of strongly correlated electron matter.
Motivated by the recent experimental observation of an intermediate bosonic metallic state in the two-dimensional superconductor-insulator transition at T=0T=0T=0, we study an extended Bose-Hubbard model in the limit of a large number of particles per site. Using a representation of this in terms of two coupled XYXYXY models, we find, in addition to an insulating phase and a (2+1)D(2+1)\mathrm{D}(2+1)D superfluid phase, two other phases. One phase is a 2D superfluid phase where a crossover from (2+1)D(2+1)\mathrm{D}(2+1)D to 2D has taken place as a result of incipient charge ordering, signaled by $\ensuremath{\theta}$ disordering, and which is closely related to a supersolid phase. The other new phase is an edge metal state characterized by zero superfluid stiffness, zero charge ordering, and zero bulk compressibility. However, the edge compressibility of the system is nonzero. While we do not find any intermediate state with 2D metallic conductivity, we are able to connect these results to STM experiments on MoS2{\mathrm{MoS}}_{2}MoS2​ showing brims of finite density of states around the entire edge of 2D MoS2{\mathrm{MoS}}_{2}MoS2​ samples.
We carry out an extensive study of the phase diagram of the extended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it can have Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases depending on the precise value of filling and how edge states are handled. We show that the critical exponents and central charge for the HI-DW, MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) universality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition.
Topology of the Fermi surface and universality of the metal-metal and metal-insulator transitions: ddd-dimensional Hatsugai-Kohmoto model as an example
The earlier theory [1] of the quantum phase transitions related to the change of the Fermi Surface Topology (FST) is advanced. For such transitions the Fermi surface as a quantum critical manifold determined by the Lee-Yang zeros, the order parameter P\mathcal{P}P as the ddd-volume of the Fermi sea, and the special FST universality class were introduced in [1]. The exactly solvable Hatsugai-Kohmoto (HK) ddd-dimensional (d=1,2,3d=1,2,3d=1,2,3) model of interacting fermions is analyzed. We explore the relation between the Lee-Yang zeros, the Luttinger and the plateau (Oshikawa) theorems. The validity of the Luttinger theorem in the HK model is confirmed. It is shown that the order parameter P\mathcal{P}P and the FST universality class describe the transitions between metal and band/Mott insulators, as well as the Lifshitz and van Hove gapless-to-gapless transitions. The gapless phases are established to be the Landau Fermi liquids (metals). In addition to the conventional paradigm with a continuous order parameter, we apply the homology theory to analyze the FST transitions. They are critical points of the Morse function. To quantify FST we use the Euler characteristic, which is calculated for each phase of the HK model. We claim that the FST universality class is robust with respect to interactions and other model details, under the condition that the critical points are non-degenerate.
We carry out an extensive study of the phase diagrams of the extended Bose Hubbard model, with a mean filling of one boson per site, in one dimension by using the density matrix renormalization group and show that it contains Superfluid (SF), Mott-insulator (MI), density-wave (DW) and Haldane-insulator (HI) phases. We show that the critical exponents and central charges for the HI-DW, MI-HI and SF-MI transitions are consistent with those for models in the two-dimensional Ising, Gaussian, and Berezinskii-Kosterlitz-Thouless (BKT) universality classes, respectively; and we suggest that the SF-HI transition may be more exotic than a simple BKT transition. We show explicitly that different boundary conditions lead to different phase diagrams.