Although most quantum systems thermalize locally on short time scales independent of initial conditions, recent developments have shown this is not always the case. Lattice geometry and quantum mechanics can conspire to produce constrained quantum dynamics and associated glassy behavior, a phenomenon that falls outside the rubric of the eigenstate thermalization hypothesis. Constraints "fragment" the many-body Hilbert space due to which some states remain insulated from others and the system fails to attain thermal equilibrium. Such fragmentation is a hallmark of geometrically frustrated magnets with low-energy "icelike manifolds" exhibiting a broad range of relaxation times for different initial states. Focusing on the highly frustrated kagome lattice, we demonstrate these phenomena in the Balents-Fisher-Girvin Hamiltonian (easy-axis regime), and a three-coloring model (easy-plane regime), both with constrained Hilbert spaces. We study their level statistics and relaxation dynamics to develop a coherent picture of fragmentation in various limits of the XXZ model on the kagome lattice.
Using a hybrid method based on fermionic diagonalization and classical Monte Carlo, we investigate the interplay between itinerant and localized spins, with competing double- and super-exchange interactions, on a honeycomb lattice. For moderate superexchange, a geometrically frustrated triangular lattice of hexagons forms spontaneously. For slightly larger superexchange a dimerized groundstate is stable that has macroscopic degeneracy. The presence of these states on a non-frustrated honeycomb lattice highlights a novel phenomenon in this itinerant electron system: emergent geometrical frustra…
Magnetic skyrmions have been receiving growing attention as potential information storage and magnetic logic devices since an increasing number of materials have been identified that support skyrmion phases. Explorations of artificial frustrated systems have led to new insights into controlling and engineering new emergent frustration phenomena in frustrated and disordered systems. Here, we propose a skyrmion spin ice, giving a unifying framework for the study of geometric frustration of skyrmion crystals in a non-frustrated artificial geometrical lattice as a consequence of the structural con…
We expand the concept of frustration in Mott insulators and quantum spin liquids to metals with flat bands. We show that when inter-orbital hopping $t_2$ dominates over intra-orbital hopping $t_1$, in a multiband system with strong spin-orbit coupling $λ$, electronic states with a narrow bandwidth $W\sim t_2^2/λ$ are formed compared to a bandwidth of order $t_1$ for intra-orbital hopping. We demonstrate the evolution of the electronic structure, Berry phase distributions for time-reversal and inversion breaking cases, and their imprint on the optical absorption, in a tight binding model of $d$…
So far the physics of moiré graphene bilayers at large, incommensurate rotation angles has been considered uninteresting. It has been held that the interlayer coupling in such structures is weak and the system can be thought of as a pair of decoupled single graphene sheets to a good approximation. Here, we demonstrate that for large rotation angles near commensurate ones, the interlayer coupling, far from being weak, is able to completely localize electrons to within a large scale, geometrically frustrated network of topologically protected modes. The emergent geometric frustration of the syst…
Although initially introduced to mimic the spin-ice pyrochlores, no artificial spin ice has yet exhibited the expected degenerate ice-phase with critical correlations similar to the celebrated Coulomb phase in the pyrochlore lattice. Here we study a novel artificial spin ice based on a vertex-frustrated rather than pairwise frustrated geometry and show that it exhibits a quasicritical ice phase of extensive residual entropy and, significantly, algebraic correlations. Interesting in its own regard as a novel realization of frustration in a vertex system, our lattice opens new pathways to study …
A skyrmion crystal (SkX) expressed as a multiple number of spiral modulations manifests itself not only in its peculiar magnetic texture but also in nontrivial transport properties originating from an emergent magnetic field. We here report our numerical results for multiple SkXs in a centrosymmetric tetragonal crystal system. By performing simulated annealing for an effective spin model for itinerant magnets, we find that three types of the SkXs with the skyrmion numbers of one and two, which are characterized by different superpositions of helices, are stabilized in the ground state, and are…
Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site $U$ and nearest-neighbor $V$ Coulomb interactions at $3/4$ filling ($n=3/2$) and (ii) the triangular lattice with on-site $U$, nearest-neighbor $V$, and next-nearest-neighbor $V'$ Coulomb interactions at $3/8$ filling ($n=3/4$). We consider various approaches including mean-field approximat…
The kagome lattice -- a two-dimensional (2D) arrangement of corner-sharing triangles -- is at the forefront of the search for exotic states generated by magnetic frustration. Such states have been observed experimentally for Heisenberg and planar spins. In contrast, frustration of Ising spins on the kagome lattice has previously been restricted to nano-fabricated systems and spin-ice materials under applied magnetic field. Here, we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scatte…
We investigate emergent quantum dynamics of the tilted Ising chain in the regime of a weak transverse field. Within the leading order perturbation theory, the Hilbert space is fragmented into exponentially many decoupled sectors. We find that the sector made of isolated magnons is integrable with dynamics being governed by a constrained version of the XXZ spin Hamiltonian. As a consequence, when initiated in this sector, the Ising chain exhibits ballistic transport on unexpectedly long times scales. We quantitatively describe its rich phenomenology employing exact integrable techniques such as…
A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod kagome lattice material Ho3Mg2Sb3O14 unites an ice-like magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, realizing a frustrated transverse Ising model. Using neutron scattering and thermodynamic experiments, we observe a…
In this work, based on the Fredkin spin chain, we introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the 1D Fermi-Hubbard model in the infinite onsite repulsion limit. To demonstrate the many-body scars, we construct an exact eigenstate that is in the middle of the spectrum within each fractured sub-sector displaying either logarithmic or area-law entanglement entropy. The in…
We propose an entanglement-enhanced sensing scheme that is robust against spatially inhomogeneous always-on Ising interactions. Our strategy is to tailor coherent quantum dynamics employing the Hilbert-space fragmentation (HSF), a recently recognized mechanism that evades thermalization in kinetically constrained many-body systems. Specifically, we analytically show that the emergent HSF caused by strong Ising interactions enables us to design a stable state where part of the spins is effectively decoupled from the rest of the system. Using the decoupled spins as a probe to measure a transvers…
A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod kagome lattice material Ho${_3}$Mg${_2}$Sb${_3}$O${_{14}}$ unites an ice-like magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho$^{3+}$ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodyna…
The highly frustrated Heisenberg antiferromagnet on Checkerboard and Pyrochlore lattices is subject to strong quantum fluctuations. This problem is amenable to the Contractor Renormalization (CORE) algorithm, which systematically computes the effective interactions in a basis of local cluster eigenstates. CORE was recently used to derive the Plaquette Boson-Fermion model for the square lattice Hubbard model (cond-mat/0108087). For the spin half Checkerboard and Pyrochlore cases, we find singlet ground states which break lattice symmetry, and a gap to spin one excitations. The low excitations a…
Employing the self-learning quantum Monte Carlo algorithm, we investigate the frustrated transverse-field triangle-lattice Ising model coupled to a Fermi surface. Without fermions, the spin degrees of freedom undergoes a second-order quantum phase transition between paramagnetic and clock-ordered phases. This quantum critical point (QCP) has an emergent U(1) symmetry and thus belongs to the (2+1)D XY universality class. In the presence of fermions, spin fluctuations introduce effective interactions among fermions and distort the bare Fermi surface towards an interacting one with hot spots and …
The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in $d$-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective non-integrable model with $d\geq2$ as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for non-equi…
We investigate the effect of geometrical frustration on the competition between the Kondo coupling and the Ruderman-Kittel-Kasuya-Yosida interaction in Kondo lattice systems. By variational Monte Carlo simulations, we reveal an emergent quantum phase with partial ordering in which the frustration is relieved by forming a magnetic order on a sublattice and leaving the rest in the Kondo screening with spin-singlet formation. The role of quantum fluctuations and spin-charge interplay is elucidated.
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalised set of few-body coherent states. In particular, model Hamiltonians of the FQH effect are equivalent to the real space von Neumann lattice of local projection operators imposed on a continuous system in the thermodynamic limit. It can be analytically derived that tuning local one-body potentials in such lattices amounts to the tuning of individual two or few-body pseudopotentials. For some cases, we can realise pure few-body pseudopotentials important for stabilisin…
We examine instabilities of the plateau phases in the spin-1/2 kagome-lattice antiferromagnet in an applied field by means of degenerate perturbation theory, and find some emergent supersolid phases below the $m=5/9$ plateau. The wave functions of the plateau phases in a magnetic field have the particular construction based on the building blocks of resonating hexagons and their surrounding sites. Magnon excitations on each of these blocks suffer from a kinetic frustration effect, namely, they cannot hop easily to the others since the hopping amplitudes through the two paths destructively canc…
Emergent Vortex Ordering in a Multiflavor Pyrochlore-Lattice Compound GeCo$_2$O$_4$
University of Science and Technology of China（中国科学技术大学）；Comprehensive Research Organization for Science and Society (CROSS)（综合研究组织科学社会）；Rutherford Appleton Laboratory（鲁瑟福阿普顿实验室）；Peking University（北京大学）；China Institute of Atomic Energy（中国原子能科学研究院）
We explore the frustrated spin-$1/2$ Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) inter-triangle couplings ($J_e<0$), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening $J_e$, the system s…
Coupling dynamical charges to gauge fields can result in highly non-local interactions with a linear confining potential. As a consequence, individual particles bind into mesons which, in one dimension, become the new constituents of emergent Luttinger liquids. Furthermore, at commensurate fillings, different Mott-insulating states can be stabilized by including nearest-neighbour (NN) interactions among charges. However, rich phase diagrams expected in such models have not been fully explored and still lack comprehensive theoretical explanation. Here, by combining numerical and analytical tool…
Frustration effects on the magnetization plateau physics in a trimerized quantum spin-1/2 chain
Instituto de Física, Universidade Federal de Mato Grosso do Sul（南马托格罗索联邦大学物理研究所）；Departamento de Física, Universidade Federal de Santa Maria（圣玛丽亚联邦大学物理系）
Interleaved bond frustration in a triangular lattice antiferromagnet
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Technical University of Munich（慕尼黑工业大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Cornell High Energy Synchrotron Source, Cornell University（康奈尔大学高能同步辐射光源，康奈尔大学）；Advanced Photon Source, Argonne National Laboratory（阿贡国家实验室先进光子源）
We report a combined experimental and theoretical study of KCuF3, which offers - because of this material's relatively simple lattice structure and valence configuration (d9, i.e., one hole in the d-shell) - a particularly clear view of the essential role of the orbital degree of freedom in governing the dynamical coupling between the spin and lattice degrees of freedom. We present Raman and x-ray scattering evidence that the phase behaviour of KCuF3 is dominated above the Neel temperature (T_N = 40 K) by coupled orbital/lattice fluctuations that are likely associated with rotations of the CuF…
The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2)$_{\rm{spin}} \otimes $U(1)$_{\rm{charge}}$ symmetries implemented, we study the triangular-lattice Hubbard model defined on the long cylinder geometry up to circumference $W=6$. A gapped quantum spin liquid, with on-site interaction $9 \lesssim U / t \lesssim 10.75$, is identified between the metallic …
Rydberg atoms in optical tweezer arrays provide a playground for nonequilibrium quantum many-body physics. The PXP model describes the dynamics of such systems in the strongly interacting Rydberg blockade regime and notably exhibits weakly nonergodic dynamics due to quantum many-body scars. Here, we study the PXP model in a strong staggered external field, which has been proposed to manifest quasiparticle confinement in light of a mapping to a lattice gauge theory. We characterize this confining regime using both numerical exact diagonalization and perturbation theory around the strong-field l…
Spin-1/2 maple leaf lattice antiferromagnets are expected to show interesting phenomena originating from frustration effects and quantum fluctuations. We report the hydrothermal synthesis of a powder sample of bluebellite Cu$_6$IO$_3$(OH)$_{10}$Cl as a first potential candidate. Magnetization and heat capacity measurements reveal moderate frustration with a Curie-Weiss temperature of $-35$ K, and a magnetic transition at $T_N$ = 17 K. Surprisingly, the magnetic susceptibility and heat capacity above $T_N$ are well reproduced by the Bonner-Fisher model, which suggests that a one-dimensional spi…
The fully frustrated ladder - a quasi-1D geometrically frustrated spin one half Heisenberg model - is non-integrable with local conserved quantities on rungs of the ladder, inducing the fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets and whose persistence i…
Frustrated systems are ubiquitous and interesting because their behavior is difficult to predict. Magnetism offers extreme examples in the form of spin lattices where all interactions between spins cannot be simultaneously satisfied. Such geometrical frustration leads to macroscopic degeneracies, and offers the possibility of qualitatively new states of matter whose nature has yet to be fully understood. Here we have discovered how novel composite spin degrees of freedom can emerge from frustrated interactions in the cubic spinel ZnCr2O4. Upon cooling, groups of six spins self-organize into we…
Fractionalization from Kinetic Frustration in Doped Two-Dimensional SU(4) Quantum Magnets
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Institute for Theoretical Physics, ETH Zurich（苏黎世联邦理工学院理论物理研究所）
Frustration-driven topological textures on the honeycomb lattice: antiferromagnetic meron-antimeron and skyrmion crystals emerging from spiral spin liquids
Geometric fragmentation and anomalous thermalization in cubic dimer model
German Aerospace Center (DLR), Institute of Frontier Materials on Earth and in Space, Functional, Granular, and Composite Materials（德国航空航天中心前沿地球与空间材料研究所功能颗粒及复合材料部门）；University of Southampton（南安普顿大学）；Wake Forest University（维克森林大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；TNG Technology Consulting GmbH（TNG技术咨询有限公司）
We demonstrate the existence of orbital Coulomb phase as the exact ground state of p-orbital exchange Hamiltonian on the diamond lattice. The Coulomb phase is an emergent state characterized by algebraic dipolar correlations and a gauge structure resulting from local constraints (ice rules) of the underlying lattice models. For most ice models on the pyrochlore lattice, these local constraints are a direct consequence of minimizing the energy of each individual tetrahedron. On the contrary, the orbital ice rules are emergent phenomena resulting from the quantum orbital dynamics. We show that t…
Multi-orbital optical lattices have been attracting rapidly growing research interests in the last several years, providing fascinating opportunities for orbital-based quantum simulations. Here, we consider bosonic atoms loaded in the degenerate $p$-orbital bands of a two-dimensional triangular optical lattice. This system is described by a multi-orbital Bose-Hubbard model. We find the confined atoms in this system develop spontaneous orbital polarization, which forms a chiral Skyrmion lattice pattern in a large regime of the phase diagram. This is in contrast to its spin analogue which largel…
Search for a new quantum state of matter emerging in a crystal is one of recent trends in condensed matter physics. For magnetic materials, geometrical frustration and high magnetic field are two key ingredients to realize it: a conventional magnetic order is possibly destroyed by competing interactions (frustration) and is replaced by an exotic state that is characterized in terms of quasiparticles, that are magnons, and the magnetic field can control the density and chemical potential of the magnons. Here we show that a synthetic copper mineral, Cd-kapellasite, comprising a kagome lattice ma…
