Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session R07: Mott Insulators and the Hubbard ModelFocus

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Sponsoring Units: DCMP Chair: Bruce Normand, Paul Scherrer Institute Room: BCEC 109B 
Thursday, March 7, 2019 8:00AM  8:12AM 
R07.00001: Finitetemperature charge dynamics and the melting of the Mott insulator Bruce Normand, XingJie Han, Chuang Chen, Jing Chen, HaiDong Xie, RuiZhen Huang, HaiJun Liao, Zi Yang Meng, Tao Xiang The Mott insulator is the quintessential strongly correlated electronic state. A full understanding of the coupled charge and spin dynamics of the Mottinsulating state is thought to be the key to a range of phenomena in ultracold atoms and condensed matter, including highT_{c} superconductivity. Here we extend the slavefermion (holondoublon) description of the twodimensional Mott insulator to finite temperatures. We benchmark its predictions against stateoftheart quantum Monte Carlo simulations, finding quantitative agreement. Qualitatively, the shortranged spin fluctuations at any finite temperatures are sufficient to induce holondoublon bound states, and renormalize the charge sector to form the Hubbard bands. The Mott gap is understood as the charge (holondoublon) gap renormalized downwards by these spin fluctuations. With increasing temperature, the Mott gap closes while the charge gap remains finite, causing a pseudogap regime to appear naturally during the process of melting the Mott insulator. 
Thursday, March 7, 2019 8:12AM  8:24AM 
R07.00002: Local Density distribution of disordered BoseHubbard Model K Hettiarachchilage, C Moore, V. G Rousseau Rousseau, KaMing Tam, Mark Jarrell, J Moreno We study the local density of the BoseHubbard model in the presence of onsite disorder in the canonical ensemble. At incommensurate filling, our findings support the scenario of percolating superfluid clusters enhancing Anderson localization. Scaling analysis of the superfluid density at the incommensurate filling of ρ=1.1 and onsite interaction U=80t predicts a superfluidBose glass transition at disorder strength of Δ_{c}~30t. At this filling, the local density distribution becomes more skew with increasing disorder strength. In the Bose glass phase, the mode of the local density distribution approaches an integer value as expected from typical medium theory for the Anderson localization. On the other hand, the behavior at commensurate filling is rather different. Close to the tip of the Mott lobe ρ=1, U=22t we find a Mott insulatorBose glass transition at disorder strength of Δ_{c}~16t. An analysis of the local density distribution shows Gaussian like behavior for a wide range of disorders above and below the transition. 
Thursday, March 7, 2019 8:24AM  8:36AM 
R07.00003: Resonant Driving induced Ferromagnetism in the Fermi Hubbard Model Ning Sun, Pengfei Zhang, Hui Zhai In this letter we consider quantum phases and the phase diagram of a Fermi Hubbard model under periodic driving that has been realized in recent cold atom experiments, in particular, when the driving frequency is resonant with the interaction energy. Due to the resonant driving, the effective Hamiltonian contains a correlated hopping term where the density occupation strongly modifies the hopping strength. Focusing on half filling, in addition to the charge and spin density wave phases, large regions of ferromagnetic phase and phase separation are discovered in the weakly interacting regime. The mechanism of this ferromagnetism is attributed to the correlated hopping because the hopping strength within a ferromagnetic domain is normalized to a larger value than the hopping strength across the domain. Thus, the kinetic energy favors a large ferromagnetic domain and consequently drives the system into a ferromagnetic phase. We note that this is a different mechanism in contrast to the wellknown Stoner mechanism for ferromagnetism where the ferromagnetism is driven by interaction energy. 
Thursday, March 7, 2019 8:36AM  8:48AM 
R07.00004: Charge Density Waves in a Doped Kondo Chain Yixuan Huang, Donna Sheng, ChinSen Ting We show that charge density waves (CDWs) exist in the ground state of the onedimensional Kondo lattice model at the filling of n=0.75 with a finite charge gap, while most of the doped phase is metallic. Based on our numerical results using the density matrix renormalization group method, we separate the CDW phase from the paramagnetic phase previously known as the TomonagaLuttinger liquid. The emergence of this phase serves as an example of CDW induced without repulsive interaction between electrons, and enriches the phase diagram of the 1D Kondo Lattice model. 
Thursday, March 7, 2019 8:48AM  9:00AM 
R07.00005: The spectral function of Mottinsulating Hubbard ladders: From fractional excitations to coherent quasiparticles Chun Yang, Adrian Feiguin We study the spectral function of twoleg Mott insulating Hubbard ladders using the timedependent density matrix renormalization group method (tDMRG). The spectrum displays features of both spincharge separation and coherent bound states. As the interleg hopping is increased, both spin and hole branches merge into a single coherent quasiparticle band and the spectrum undergoes a crossover from a regime with two incommensurate minima, to one with a single minimum. At the same time, the system shifts from a Mott insulator to a band insulator. Interestingly, while the bonding sector of the spectrum realizes quasiparticles, the antibonding one displays a broad low energy scattering continuum, which can be associated to the lack of quasiparticles. We identify the processes leading to quasiparticle formation by studying the time evolution of charge and spin degrees of freedom in real space after a hole is created. At short times, incoherent holons and spinons are emitted but charge and spin quickly form polarons that propagate coherently. 
Thursday, March 7, 2019 9:00AM  9:12AM 
R07.00006: The Hall conductivity in correlated electron systems Georg Rohringer, Anton Markov, Alexey Rubtsov The Hall conductivity describes the response current perpendicular to the direction of an 
Thursday, March 7, 2019 9:12AM  9:24AM 
R07.00007: Scaling theory for MottHubbard transitions Anirban Mukherjee, Siddhartha Lal We present a zero temperature nonperturbative analytical renormalization group (RG) investigation of the electronic Hubbard model in two dimensions on a square lattice. The source of quantum fluctuations in the occupation number of an electronic state is driven by elements of the Hubbard Hamiltonian that are offdiagonal in the Fock representation. Our RG resolves these quantum fluctuations via an iterative scheme involving the unitarily decoupling of an electronic state at every RG step. Stable fixed points of the RG identify effective Hamiltonians associated with various phases as a function of the fluctuation energy scale and doping. We find that the halffilled Mott transition involves passage from a gapless nonFermi liquid to a gapped Mott liquid through a pseudogapped phase upon lowering the fluctuation scale. Upon doping, we show the collapse of the Mott liquid at a quantum critical point possessing dwave structure in kspace: a nodal nonFermi liquid with large superconducting fluctuations, and preformed Cooper pairs lying within spinpseudogapped parts of kspace located away from the nodes. By allowing for symmetry breaking, we find an emergent dwave superconducting phase surrounding the quantum critical point. This work is available at arXiv:1802.06528. 
Thursday, March 7, 2019 9:24AM  9:36AM 
R07.00008: Rectification in Mottinsulator pn junctions Zekun Zhuang, jaime merino, John Marston AC currents are typically rectified by semiconducting pn junctions. Here, we theoretically explore the possibility of realizing a rectifier based on a doped Mottinsulator pn junction. First, we obtain the time dependence of a dissipationless Mott pn junction along onedimensional chains modeled by a Hubbard model and an extended Hubbard model. We numerically integrate the manybody Schrodinger equation in time and show that rectification only occurs when both Coulomb repulsion and inversion symmetry breaking are simultaneously present. We then show how rectification is also captured when the Hubbard interaction is treated within a timedependent HartreeFock (TDHF) approximation. Finally, we analyze the effect of dissipation in the Mott pn junction by combining the timedependent HartreeFock (TDHF) approximation with the Lindblad equation. This permits investigation of the transport properties of realistic threedimensional junctions that can be compared to experimental observations. 
Thursday, March 7, 2019 9:36AM  9:48AM 
R07.00009: Prediction of Mott insulation and atomic displacements in 3d ABO_{3} oxide perovskites without Hubbard U Julien Varignon, Manuel Bibes, Alex Zunger The existence of insulating band gaps in both spinordered and disordered phases of 3d ABO_{3} perovskite oxides has been traditionally ascribed within the Mott picture to the formation of a twoelectron state on a 3d site and an empty 3d site; the separation between these upperHubbard and lowerHubbard states is the interelectronic repulsion U. The observed structural distortions such as bond disproportionation or JahnTeller motions appear as secondary effects. The nonspin polarized DFT approach gives zero gap, a result that was used in the literature as a basis to argue that DFT fails. We apply to all ABO_{3} 3d perovskites DFT with (i) fully relaxed large supercells (ii) using XC functionals that have small delocalization errors (DFT+U and SCAN without U) and (iii) occupying single partners in degenerate levels. We find DFT even without U capture gapping trends and structural distortions in ABO_{3} materials ranging from titanates to nickelates in both AFM and PM phases. Our results thus suggest that dynamical correlations are not playing a universal role in gapping of 3d ABO_{3} insulators, and demonstrate that DFT is a viable platform fully able to model their ground states. 
Thursday, March 7, 2019 9:48AM  10:00AM 
R07.00010: Mott transitions in a class of solvable models Wayne Zheng, YuanMing Lu We construct a class of lattice models, where an electronic superconductor can be driven into a fractionalized Mott insulator by increasing the onsite Coulomb repulsion. We obtain the exact ground states of these models and study their quantum critical phenomena using quantum Monte Carlo simulations. 
Thursday, March 7, 2019 10:00AM  10:12AM 
R07.00011: Nature of Mott Insulator in 2D Hubbard Model by Eliashberg Theory Jose Rodriguez, Geovani A Montoya We introduce an Eliashberg theory in the particlehole channel for the Hubbard model over the square lattice that exploits the perfect nesting shown by the Fermi surface at half filling[1]. It results in Eliashberg equations for the wavefunction renormalization 1/Z and for the gap Δ_{SDW} in quasiparticle excitations at half filling. They are solved within the approximation that the corners of the diamond Fermi surface control the physics at half filling. We find that the wavefunction renormalization 1/Z vanishes as (t/U)^{2} at strong onsite repulsion U compared to the hopping matrix element t. By comparison with mean field theory, the SDW gap is accordingly reduced down in size by the wavefunction renormalization to Δ_{SDW} ∼ t^{2}/U. In other words, the SDW gap is of order the antiferromagnetic exchange coupling constant J. These results will be checked against direct numerical solutions of the former Eliashberg equations. 
Thursday, March 7, 2019 10:12AM  10:24AM 
R07.00012: Local entropies across the Mott transition in an exactly solvable model Luke Yeo, philip Phillips Spatial entanglement is a natural probe of delocalisation across metalinsulator transitions, but little is known of its behaviour in two or three dimensions near interactiondriven Mott transitions. We address this problem for the exactly solvable HatsugaiKohmoto model, whose Mott transition occurs at zero temperature between classically mixed states. We find that both its singlesite entropy and its classical entropy density exhibit kinks at the Mott transition, only in one and two dimensions. Although the variation in entropy density across the transition dominates in the thermodynamic limit, the singlesite entropy increases even as the degree of classical mixing is decreased. This suggests that the HatsugaiKohmoto model maintains quantumcoherent delocalisation even in the presence of classical mixing. 
Thursday, March 7, 2019 10:24AM  10:36AM 
R07.00013: Hidden spin current in doped Mott antiferromagnets Wayne Zheng, Zheng Zhu, Donna Sheng, ZhengYu Weng We investigate the nature of doped Mott insulators using exact diagonalization and density matrix renor malization group methods. Persistent spin currents are revealed in the ground state, which are concomitant with a nonzero total momentum or angular momentum associated with the doped hole. The latter determines a nontrivial ground state degeneracy. By further making superpositions of the degenerate ground states with zero or unidirectional spin currents, we show that different patterns of spatial charge and spin modulations will emerge. Such anomaly persists for the odd numbers of holes, but the spin current, ground state degeneracy, and charge/spin modulations completely disappear for even numbers of holes, with the twohole ground state exhibiting a dwave symmetry. An understanding of the spin current due to a manybody Berrylike phase and its influence on the momentum distribution of the doped holes will be discussed. 
Thursday, March 7, 2019 10:36AM  10:48AM 
R07.00014: Doping a 2d Mott insulator – Study of a quantum dimer model Sebastian Huber, Fabian Grusdt, Matthias Punk Experiments with quantum gas microscopes have started to explore the antiferromagnetic phase of the FermiHubbard model and effects of doping with holes away from half filling^{1}. We show in this talk that the system averaged local twospin density matrix enables to distinguish magnetically ordered and interesting topologically ordered spinliquid phases, which might occur in the Hubbard model close to half filling. 
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