Exotic Quantum States In Solvable Models

Since the discovery of high-T_csuperconductivity in cuprates in 1986,al-though intensive experimental researches have been carried out,the high-T_cis still the key puzzle in modern condensed matter physics.The difficulty lies in its com-plex phase diagram,especially in the high temperature region,where various or-ders compete with each other and thus leading to unconventional behaviors beyond the Landau's Fermi liquid theory.The strong correlation defies exact theoretical solution in the correlated electron system.Even for the simplest Hubbard model with only onsite correlation,the exact solution is not accessible when d?2.Therefore,the study of solvable many-body models plays a fundamental role in understanding exotic quantum states beyond the Landau's Fermi liquid theory.In spatial dimension d>1,Kitaev's toric-code,honeycomb model and certain Z₂lattice gauge field models are prototypical examples,which shows novel quan-tum orders like Majorana quantum spin liquid,orthogonal metal,fractionalized Chern insulator,fracton order,Majorana superconductor and many-body localized state.However,because of the designed local gauge symmetry,these models are far from the standard ones in condensed matter physics like Hubbard and Kondo lattice models.Thus,in this paper we instead study some solvable models with-out any fine-tuning local gauge structure,i.e.,the Ising-Kondo(IK)model and the Falicov-Kimball model.They are not only solvable,but can also describe the generic interaction of the real materials,e.g.,the heavy fermion compounds and cuprates.The IK model is a Kondo lattice model in its anisotropic limit,whereas the FK model is the alternative spinless Hubbard model.By unbiased Monte Carlo simulation,the IK and FK model are solvable for arbitrary lattice geometry,spatial dimension and electron filling,where various exotic quantum states are discovered.Here,we carry out the following studies:(i)We carry out a case study of the IK model on square lattice,which shows that the ground state is a Néel antiferromagnetic insulator at half-filling.At fi-nite temperature,paramagnetic phases including a Mott insulator and correlated metal are found.The former is a melting antiferromagnetic insulator with a strong short-range magnetic fluctuation,while the latter corresponds to a Fermi liquid-like metal.Monte Carlo simulation and theoretical analysis demonstrate that the transi-tion from paramagnetic phases into the antiferromagnetic insulator is a continuous2D Ising transition.Away from half-filling,patterns of spin stripes(inhomoge-neous magnetic order)at weak coupling,and phase separation at strong coupling are predicted.With established Ising antiferromagnetism and spin stripe orders,our model may be relevant to a heavy fermion compound Ce Co(In_1-xHg_x)₅and novel quantum liquid-crystal order in a hidden order compound URu₂Si₂.(ii)Besides,the Mn Bi₂Te₄material which proposed as the first intrinsic an-tiferromagnetic topological insulator(AFMTI)can also be described by the alter-native IK model.The interplay between magnetism and topology induces several fascinating topological phases,such as the quantum anomalous Hall effect,Majo-rana fermions,and axion electrodynamics.However,an exactly solvable model being capable to capture the essential physics of the interplay between magnetism and topology is still absent.Here,inspired by the the Ising-like nature and the topological property of Mn Bi₂Te₄,we propose a topological Ising-Kondo lattice(TIKL)model to study its ground state property in an analytical way at zero temper-ature.The resultant phase diagram includes rich topological and magnetic states,which emerge in the model proposed in a natural and consistent way for the intrin-sic magnetic topological insulator.With Monte Carlo simulation,we extend the AFMTI ground state to finite temperature.It reveals that topological properties do sustain at high temperature,which even can be restored by elevated temperature at suitable correlation strength.The results demonstrate that TIKL may offer an insight for future experimental research,with which magnetism and transport prop-erties could be fine tuned to achieve more stable and exotic magnetic topological quantum states.(iii)Above studies suggest the half-filled IK model can access to robust Mott physics under strong correlation,which closely connected to the cuprates.Thus we further solve the doped Mott insulator in the IK model,which unambiguously exhibits strange metal phenomena accompanied with quantum critical scaling in observables,e.g.resistivity,susceptibility and specific heat.Besides,we reveal three different metallic states with unconventional transports and thermodynamics in the high-temperature region,which all exhibit robust non-Fermi liquid feature.Our study suggests that SM,Mott quantum criticality are the intrinsic features of doped Mott insulator,which are promising to be revealed in generic strongly cor-related electron systems.(iv)Finally,we try to further study the microscopic mechanism of the above-mentioned robust non-Fermi liquid nature in the IK model.Closer look at SM reveals the breakdown of Landau's Fermi liquid without any symmetry-breaking,i.e.the violation of Luttinger's theorem.The Luttinger's theorem has long been taken as the key feature of Landau's Fermi liquid,which signals the presence of quasiparticles.Examining electron's self-energy extracted from numerical simu-lation provides the explanation on the origin of linear-T resistivity and suggests that the long-overlooked static fluctuations in literature play an essential role in non-Fermi liquid behaviors in correlated electron systems.Compared with results of the FK model,we find in both models the violation of Luttinger's theorem is robust under any electron density.Introducing hole carriers to the half-filled FK leads to Mott insulator-metal transition,where the Mott quantum criticality man-ifests unconventional scaling behavior in transport properties.Further insight on the violation of the Luttinger's theorem is examined by combining Hubbard-I ap-proximation with a composite fermion picture,which emphasizes the importance of a mixed excitation of the itinerant electron and the composite fermion.Interest-ingly,when compared FK model with a binary disorder system,it suggests that the two-peak band structure discovered by Monte Carlo and Hubbard-I approaches is underlying the violation of Luttinger's theorem.We hope the unbiased studies on the IK model and FK model can improve the understanding of the exotic quantum states beyond Landau's Fermi liquid theory.