Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that most of the topological indices defined for free electron systems are very likely unsuitable for interacting cases. In this work, we demonstrate that the strange correlator is a sensitive diagnosis to detect SPT states in interacting systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we investigate the interaction-driven quantum phase transition in the Kane-Mele-Hubbard model. The transition from the quantum spin Hall insulator at weak interaction to an antiferromagnetic Mott insulator at strong interaction can be readily detected by the momentum space behavior of the strange correlator in single-particle, spin, and pairing sectors. The interaction effects on the symmetry-protected edge states in various sectors, i.e., the helical Luttinger liquid behavior, are well captured in the QMC measurements of strange correlators. Moreover, we demonstrate that the strange correlator is technically easier to implement in QMC and more robust in performance than other proposed numerical diagnoses for interacting topological states, as only static correlations are needed. The attempt in this work paves the way for using the strange correlator to study interaction-driven topological phase transitions in fermionic as well as bosonic systems.
We employ strange correlators to detect 2D subsystem symmetry-protected topological (SSPT) phases which are nontrivial topological phases protected by subsystem symmetries. Specifically, we analytically construct efficient strange correlators in the 2D cluster model in the presence of a uniform magnetic field and then perform the projector Quantum Monte Carlo simulation within the quantum annealing scheme. We find that strange correlators show the long-range correlation in the SSPT phase, from which we define strange order parameters to characterize the topological phase transition between the…
We demonstrate the following conclusion: If $|Ψ\rangle$ is a $1d$ or $2d$ nontrivial short range entangled state, and $|Ω\rangle$ is a trivial disordered state defined on the same Hilbert space, then the following quantity (so called strange correlator) $C(r, r^\prime) = \frac{\langle Ω|ϕ(r) ϕ(r^\prime) | Ψ\rangle}{\langle Ω| Ψ\rangle}$ either saturates to a constant or decays as a power-law in the limit $|r - r^\prime| \rightarrow +\infty$, even though both $| Ω\rangle$ and $| Ψ\rangle$ are quantum disordered states with short-range correlation. $ϕ(r)$ is some local operator in the Hilbert sp…
The Hubbard model with additional intersite interaction `$V$' (the extended Hubbard model) is investigated by the correlator projection method (CPM). CPM is a newly developed numerical method which combines the equation-of-motion approach and the dynamical mean-field theory. Using this method, properties of the extended Hubbard Model at quarter filling are discussed with special emphasis on the metal-insulator transition induced by electron-electron correlations. The result shows a metal-insulator transition to a charge ordered insulator with antiferromagnetic order at low temperatures, but a …
The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of symmetry protected topological order in one- and two-dimensional systems. It takes the form of a spin-spin correlation function, computed as a mixed overlap between the state of interest and a trivial local product state. We demonstrate that it can be computed exactly (asymptotically, in the Monte Carlo sense) for various Affleck-Kennedy-Lieb-Tasaki states by direct evaluation of the wave function within the valence bond loop gas framework. We present results for lattices with chain, square, honeycom…
Detecting underlying symmetry-protected topological phases via strange correlators and edge engineering
Beijing Normal University（北京师范大学）；Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）；The Hong Kong University of Science and Technology（香港科技大学）；Beihang University（北京航空航天大学）；Tianmushan Laboratory（天目山实验室）
We study the behavior of the recently proposed "strange correlator" [Phys. Rev. Lett. {\bf 112}, 247202 (2014)] in spin-1 Heisenberg antiferromagnetic chains with uniaxial single-ion anisotropy. Using projective quantum Monte Carlo, we are able to directly access the strange correlator in a variety of phases, as well as to examine its critical behavior at the quantum phase transition between trivial and non-trivial symmetry protected topological phases. After finding the expected long-range behavior in these two symmetry conserving phases, we go on to verify the topological nature of two-leg a…
Metallic states coined strange metal (SM), with robust linear-$T$ resistivity, have been widely observed in many quantum materials under strong electron correlation, ranging from high-$T_{c}$ cuprate superconductor, organic superconductor to twisted multilayer graphene and MoTe$_{2}$/WSe$_{2}$ superlattice. Despite decades of intensive studies, the mystery of strange metal still defies any sensible theoretical explanation and has been the key puzzle in modern condensed matter physics. Here, we solve a doped Mott insulator model, which unambiguously exhibits SM phenomena accompanied with quantu…
We study a dual flavor fermion model where each of the flavors form a Sachdev-Ye-Kitaev (SYK) system with arbitrary and possibly distinct $q$-body interactions. The crucial new element is an arbitrary all-to-all $r$-body interaction between the two flavors. At high temperatures the model shows a strange metal phase where both flavors are gapless, similar to the usual single flavor SYK model. Upon reducing temperature, the coupled system undergoes phase transitions to previously unseen phases - first, a strange half metal (SHM) phase where one flavor remains a strange metal while the other is g…
Filling-control metal-insulator transition on the two-dimensional Hubbard model is investigated by using the correlator projection method, which takes into account momentum dependence of the free energy beyond the dynamical mean-field theory. The phase diagram of metals and Mott insulators is analyzed. Lifshitz transitions occur simultaneously with metal-insulator transitions at large Coulomb repulsion. On the other hand, they are separated each other for lower Coulomb repulsion, where the phase sandwiched by the Lifshitz and metal-insulator transitions appears to show violation of the Lutting…
Temperature-linear resistance at low temperatures in strange metals is an exotic characteristic of strong correlation systems, as observed in high-TC superconducting cuprates, heavy fermions, Fe-based superconductors, ruthenates, and twisted bilayer graphene. Here, we introduce a hole-doped valley-spin insulator, V-doped WSe2, with hole pockets in the valence band. The strange metal characteristic was observed in VxW1-xSe2 at a critical carrier concentration of 9.5 x 10^20 cm-3 from 150 K to 1.8 K. The unsaturated magnetoresistance is almost linearly proportional to the magnetic field. Using t…
The multi-scale entanglement renormalization ansatz (MERA) is a tensor network that can efficiently parameterize critical ground states on a 1D lattice, and also suggestively implement some aspects of the holographic correspondence of string theory on a lattice. Extending our recent work [S. Singh, Physical Review D 97, 026012 (2018); S. Singh, N. A. McMahon, and G. K. Brennen, Phys. Rev. D 97, 026013 (2018)], we show how the MERA representation of a 1D critical ground state---which has long range entanglement---can be viewed as a strange correlator: the overlap of a 2D state with short range …
We extend the concept of strange correlators, defined for symmetry-protected phases in [You et al., Phys. Rev. Lett. 112, 247202 (2014)], to topological phases of matter by taking the inner product between string-net ground states and product states. The resulting two-dimensional partition functions are shown to be either critical or symmetry broken, as the corresponding transfer matrices inherit all matrix product operator symmetries of the string-net states. For the case of critical systems, those non-local matrix product operator symmetries are the lattice remnants of topological conformal …
Colossal magnetoresistance is of great fundamental and technological significance and exists mostly in the manganites and a few other materials. Here we report colossal magnetoresistance that is starkly different from that in all other materials. The stoichiometric Mn3Si2Te6 is an insulator featuring a ferrimagnetic transition at 78 K. The resistivity drops by 7 orders of magnitude with an applied magnetic field above 9 Tesla, leading to an insulator-metal transition at up to 130 K. However, the colossal magnetoresistance occurs only when the magnetic field is applied along the magnetic hard a…
Transport in the emergent Bose liquid: Bad metal, strange metal, and weak insulator, all in one system
Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交大李政道理论与计算中心及物理与天文学院）；Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education)（人工结构与量子控制教育部重点实验室）；Shanghai Branch, Hefei National Laboratory（合肥国家实验室上海分部）
Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases
The Pennsylvania State University（宾夕法尼亚州立大学）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；Fudan University（复旦大学）；Collaborative Innovation Center of Advanced Microstructures（先进微结构协同创新中心）
Holographic strange metals are known to have a power law resistivity rising with temperature, which is reminiscent of the strange metal phases in condensed matter systems. In some holographic models, however, the exponent of the power law in the resistivity can be negative. In this case one encounters phases with diverging resistivity at zero temperature: holographic strange insulators. These states arise as a result of translational symmetry breaking in the system, which can either be strong explicit and relevant in the IR, or spontaneous, but pinned by a small explicit source. In some regard…
We introduce a Cellular Dynamical Cluster Approximation (CDCA) to study the nature of the Mott insulator-metal transition in the extended Hubbard model on a square lattice. At strong coupling, a d-wave Mott insulator is obtained. Hole doping drives a first order Mott transition to a non-Fermi (nFL) liquid metal. Remarkably, this nFL is caused by an Anderson orthogonality catastrophe at low energies due to the non-trivial competition between strong, non-local interactions and hopping. This constitutes the first explicit realisation of Anderson's Luttinger liquid idea in two dimensions. Many exp…
Even as the understanding of the mechanism behind correlated insulating states in magic-angle twisted bilayer graphene converges towards various kinds of spontaneous symmetry breaking, the metallic "normal state" above the insulating transition temperature remains mysterious, with its excessively high entropy and linear-in-temperature resistivity. In this work, we focus on the effects of fluctuations of the order-parameters describing correlated insulating states at integer fillings of the low-energy flat bands on charge transport. Motivated by the observation of heterogeneity in the order-par…
This paper describes a semiclassical field-theory approach to the topological properties of spatially featureless Affleck-Kennedy-Lieb-Tasaki type valence bond solid ground states of antiferromagnets in spatial dimensions one to three. Using nonlinear sigma models set in the appropriate target manifold and augmented with topological terms, we argue that the path integral representation of the ground-state wave functional can correctly distinguish symmetry-protected topological ground states from topologically trivial ones. The symmetry-protection feature is demonstrated explicitly in terms of …
The Sachdev-Ye-Kitaev (SYK) model describes a strange metal that shows peculiar non-Fermi liquid properties without quasiparticles. It exhibits a maximally chaotic behavior characterized by out-of-time-ordered correlators (OTOCs), and is expected to be a holographic dual to black holes. Recently, a striking similarity between the SYK model and the Hund-coupling induced spin-freezing crossover in multi-orbital Hubbard models has been pointed out. To further explore this connection, we study OTOCs for fermionic Hubbard models, which are prototypical models for strongly correlated electrons in so…
Quantum spin systems such as magnetic insulators usually show classical magnetic order, but such classical states can give way to quantum liquids with exotic entanglement through two known mechanisms of frustration: geometric frustration in lattices with triangle motifs, and spin-orbit-coupling frustration in the exactly solvable quantum liquid of Kitaev's honeycomb lattice. Here we present the experimental observation of a new kind of frustrated quantum liquid arising in an unlikely place: the magnetic insulator Ba4Ir3O10 where Ir3O12 trimers form an unfrustrated square lattice. Experimentall…
We study the physics of hard-core bosons with unfrustrated hopping (t) and nearest-neighbor repulsion (V) on the three dimensional pyrochlore lattice. At half-filling, we demonstrate that the small V/t superfluid state eventually becomes unstable at large enough V/t to an unusual insulating state which displays no broken lattice translation symmetry. Equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the Coulomb phase of a U(1) lattice gauge theory, allowing us to identify this insulator with a U(1) fractionalized Mott-i…
We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to Einstein-Maxwell theory in an asymptotically $\mathrm{AdS}_4$ spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. B…
One of the key factors that determine the fates of quantum many-body systems in the zero temperature limit is the competition between kinetic energy that delocalizes particles in space and interaction that promotes localization. While one dominates over the other in conventional metals and insulators, exotic states can arise at quantum critical points where none of them clearly wins. Here we present a novel metallic state that is realized at the antiferromagnetic (AF) quantum critical point in space dimensions three and below. At the critical point, interactions between particles are screened …
We review a recent holographic analysis arXiv:1005.4690 of charged black holes with scalar hair in view of their applications to the cuprate high temperature superconductors. We show in particular that these black holes show an interesting phase structure including critical behaviour at zero temperature or charge, describe both conductors and insulators (including holographic Mott-like insulators), generically have no residual entropy and exhibit experimentally observed scaling relations between electronic entropy, specific heat and (linear) DC resistivity. Transport properties are discussed i…
Photo-doping of Mott insulators or correlated metals can create an unusual metallic state which simultaneously hosts hole-like and electron-like particles. We study the dynamics of this state up to long times, as it passes its kinetic energy to the environment. When the system cools down, it crosses over from a bad metal into a resilient quasiparticle regime, in which quasiparticle bands are formed with separate Fermi levels for electrons and holes, but quasiparticles do not yet satisfy the Fermi liquid paradigm. Subsequently, the transfer of energy to the environment slows down significantly,…
The flat bands of magic-angle twisted bilayer graphene (MATBG) host strongly-correlated electronic phases such as correlated insulators, superconductors and a strange-metal state. The latter state, believed to be key for understanding the electronic properties of MATBG, is obscured by various phase transitions and thus could not be unequivocally differentiated from a metal undergoing frequent electron-phonon collisions. Here, we report transport measurements in superconducting MATBG in which the correlated insulator states are suppressed by screening. The uninterrupted metallic ground state sh…
We characterize the Mott insulator and Luther-Emery phases of the 1D Hubbard model through correlators that measure the parity of spin and charge strings along the chain. These non-local quantities order in the corresponding gapped phases and vanish at the critical point $U_c=0$. The Mott insulator consists of bound doublon-holon pairs, which in the Luther-Emery phase turn into electron pairs with opposite spins, both unbinding at $U_c$. The behavior of the parity correlators can be captured by an effective free spinless fermion model.
Electron--electron repulsion, on the one hand, can result in bound pair, which has heavy effective mass. On the other hand, it is also the cause of Mott insulator. We study the effect of a staggered magnetic field on a Hubbard model. We find that a bound pair with large energy bandwidth can be formed under the resonant staggered field, being the half of Hubbard repulsion strength. Accordingly, the system exhibits following dynamical behaviors: (i) When an electric field is applied, fast bound pair Bloch oscillation occurs, while a single electron is frozen. (ii) When a quenching resonant field…
Revealing the topology of quantum states via Kirkwood-Dirac quasiprobabilities
Istituto Nazionale di Ottica (INO), Consiglio Nazionale delle Ricerche（意大利国家光学研究所，意大利国家研究委员会）；European Laboratory for Non-linear Spectroscopy (LENS), Università di Firenze（欧洲非线性光谱学实验室，佛罗伦萨大学）；Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma（帕尔马大学数学、物理与信息科学系）；Gruppo Collegato di Parma, INFN-Sezione Milano-Bicocca（帕尔马联合小组，INFN米兰比可卡分部）；UdR Parma, INSTM（帕尔马研究组，意大利材料科学与技术研究中心）
A one band Hubbard model with intermediate coupling is shown to describe the two most important unusual features of a normal state: linear resistivity strange metal and the pseudogap. Both the spectroscopic and transport properties of the cuprates are considered on the same footing by employing a relatively simple postgaussian approximation valid for the intermediate couplings $U/t=1.5-4$ in relevant temperatures $T>100{\rm K}.$ In the doping range $\ p=0.1-0.3$, the value of $U$ is smaller than that in the parent material. For a smaller doping, especially in the Mott insulator phase, the coup…
The origin of strange metallic phase is shown to exist due to these two conditions---(i) the electrons are strongly interacting such that there are no band and Mott-Hubbard gaps, and (ii) the electronic energy levels are crossed in such a way that there is an electronic energy gap between two energy levels associated to two different wave functions. The theory is also exploited to explain (i) the upward- and downward-shifts in the $T$-linear resistivity curves, and (ii) the spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements of the La-Sr-Cu-O Mott insulato…
We discuss quantum phase transition by an exactly solvable model in the dual gravity setup. By considering the effect of the scalar condensation on the fermion spectrum near the quantum critical point(QCP), we find that there is a topologically protected fermion zero mode associated with the metal to insulator transition. We also show that the strange metal phase with T-linear resistivity emerges at high enough temperature as far as the gravity has a horizon. The phase boundaries are calculated according to the density of states, giving insights on structures of the phase diagram near the QCP.
We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site non-random repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et al. (arXiv:2002.07181) can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $M$ theory which generalizes the SU(2) spin symmetry to SU($M$), and obtain exponents for the electron and spin correlators which agree with those of …
We study fermions in an electrically-probed and asymptotically anti-de Sitter Schwarzschild spacetime which interact via novel chiral symmetry-preserving interactions. Computing the dual fermion two-point correlator, we show that these bulk interactions anisotropically gap Fermi surfaces of the boundary spectrum. Consequently, the interactions we devise provide holographic models for Fermi arcs seen ubiquitously in the pseudogap regime of the cuprates. Our interactions are modifications of the chiral symmetry-breaking Pauli coupling, which has previously been proposed as the holographic realiz…
In this article, we discuss the non-trivial collective charge excitations (plasmons) of the extended square-lattice Hubbard model. Using a fully non-perturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly-correlated phase. The momentum-resolved charge susceptibility is also computed on the basis of the Eucli…
Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) -- at least in one dimensional systems -- leading to a clear signal of the MBL transition in the probability distributions of energy eigenstate expectation values of local operators. For a paradigmatic model of MBL, namely the random-field Heisenberg spin chain, we consider the full probability distribution of eigenstate correlation functions across the entire phase diagram. We find gaussian distributions at weak disorder…
Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include $\mathbb{Z}_n$ chiral quantum clock models with strong zero modes related to $\mathbb{Z}_n$ parafermions. Here we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on $n=3$ where the Mott insulators are three-leg ladders. We link such ladders to $\mathbb{Z}_3$ chiral clock models by combining bosonization with general symmetry considerations. We also introduce …
Mott insulators form because of strong electron repulsions, being at the heart of strongly correlated electron physics. Conventionally these are understood as classical "traffic jams" of electrons described by a short-ranged entangled product ground state. Exploiting the holographic duality, which maps the physics of densely entangled matter onto gravitational black hole physics, we show how Mott-insulators can be constructed departing from entangled non-Fermi liquid metallic states, such as the strange metals found in cuprate superconductors. These "entangled Mott insulators" have traits in c…
We have simulated a half-filled $1D$ $p$-wave periodic Anderson model with numerically exact projector quantum Monte Carlo technique, and the system is indeed located in the Haldane-like state as detected in previous works on the $p$-wave Kondo lattice model, though the soluble non-interacting limit corresponds to the conventional $Z_{2}$ topological insulator. The site-resolved magnetization in an open boundary system and strange correlator for the periodic boundary have been used to identify the mentioned topological states. Interestingly, the edge magnetization in the Haldane-like state is …
We introduce a web of strongly correlated interacting 3+1D topological superconductors/insulators of 10 particular global symmetry groups of Cartan classes, realizable in electronic condensed matter systems, and their new SU(N) generalizations. The symmetries include SU(N), SU(2), U(1), fermion parity, time reversal and relate to each other through symmetry embeddings. We overview the lattice Hamiltonian formalism. We complete the list of field theories of bulk symmetry-protected topological invariants (SPT invariants/partition functions that exhibit boundary 't Hooft anomalies) via cobordism …
We propose the parent compound of the newly discovered superconducting nickelate Nd$_{1-x}$Sr$_{x}$NiO$_{2}$ as a self-doped Mott insulator, in which the low-density Nd-$5d$ conduction electrons couple to localized Ni-3$% d_{x^{2}-y^{2}}$ electrons to form Kondo spin singlets at low temperatures. This proposal is motivated with our analyses of the reported resistivity and Hall coefficient data in the normal state, showing logarithmic temperature dependence at low temperatures. In the strong Kondo coupling limit, we derive a generalized $t$-$J$ model with both Kondo singlets and nickel holons m…
Our current understanding of strongly correlated electron systems is based on a homogeneous framework. Here we take a step going beyond this paradigm by incorporating inhomogeneity from the beginning. Specifying to systems near the Mott metal-insulator transition, we propose a real space picture of itinerant electrons functioning in the fluctuating geometries bounded by interfaces between metallic and insulating regions. In 2+1-dimensions, the interfaces are closed bosonic strings, and we have a system of strings coupled to itinerant electrons. When the interface tension vanishes, the geometri…
We present a comprehensive dynamical mean field study of the triangular lattice moiré Hubbard model, which is believed to represent the physics of moiré bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, str…
