Unique Ground State Research Articles

Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry

We propose a geometric {approach to Lieb-Schultz-Mattis theorem for} quantum many-body systems with discrete spin-rotation symmetries and lattice inversion or rotation symmetry, but without translation symmetry assumed. Under symmetry-twisting on a $(d-1)$-dimensional plane, we find that any $d$-dimensional inversion-symmetric spin system possesses a doubly degenerate spectrum when it hosts a half-integer spin at the inversion-symmetric point. We also show that any rotation-symmetric generalized spin model with a projective representation at the rotation center has a similar degeneracy under symmetry-twisting. We argue that these degeneracies imply that {a unique symmetric gapped ground state that is smoothly connected to product states} is forbidden in the original untwisted systems -- generalized inversional/rotational Lieb-Schultz-Mattis theorems without lattice translation symmetry imposed. The traditional Lieb-Schultz-Mattis theorems with translations also fit in the proposed framework.

Quantum friction between metals in the hydrodynamic regime

In this work, we study the phenomenon of quantum friction in a system consisting on an atom moving at a constant speed parallel to a metallic plate. We use a hydrodynamic model to describe the degrees of freedom of a clean metal without internal dissipation. We model the polarizable atom as a two-level system with a unique ($l=0$) ground state and a threefold degenerate ($l=1$) excited state. We show that a quantum frictional force is present even in the absence of intrinsic damping in the metal, but that there is a threshold in the relative velocity that gives rise to such a force. In particular, we find that for friction to occur, the atom must move at a velocity larger than the effective speed of sound in the material, a condition that can be reached near empty or filled bands, where the Fermi velocity (which is proportional to the sound speed) becomes low. We provide analytical arguments to show that this result holds at all orders in perturbation theory.

Gappability Index for Quantum Many-Body Systems.

We propose an index I_{G} which characterizes the degree of gappability, namely the difficulty to induce a unique ground state with a nonvanishing excitation gap, in the presence of a symmetry G. I_{G} represents the dimension of the subspace of ambient uniquely gapped theories in the entire G-invariant "theory space." The celebrated Lieb-Schultz-Mattis theorem corresponds, in our formulation, to the case I_{G}=0 (completely ingappable) for the symmetry G including the lattice translation symmetry. We illustrate the usefulness of the index by discussing the phase diagram of spin-1/2 antiferromagnets in various dimensions, which do not necessarily have the translation symmetry.

Integer quantum Hall effect of two-component hard-core bosons in a topological triangular lattice

We study the many-body ground states of two-component hardcore bosons in topological triangular lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations, we demonstrate that at commensurate two-thirds filling per lattice site, two-component bosonic integer quantum hall (BIQH) effect emerges with the associated $\mathbf{K}=\begin{pmatrix} 0 & 1\\ 1 & 0\\ \end{pmatrix}$ matrix under strong intercomponent Hubbard repulsion. The topological nature is further elucidated by (i) a unique ground state degeneracy with a robust spectrum gap, (ii) a quantized topological Chern number matrix $\mathbf{C}=\mathbf{K}^{-1}$, and (iii) two counterpropagating edge branches. Moreover, with increasing nearest-neighbor repulsions, the ground state undergoes a first-order transition from a BIQH liquid to a commensurate solid order.

Entanglement Subvolume Law for 2D Frustration-Free Spin Systems

Let $H$ be a frustration-free Hamiltonian describing a 2D grid of qudits with local interactions, a unique ground state, and local spectral gap lower bounded by a positive constant. For any bipartition defined by a vertical cut of length $L$ running from top to bottom of the grid, we prove that the corresponding entanglement entropy of the ground state of $H$ is upper bounded by $\tilde{O}(L^{5/3})$. For the special case of a 1D chain, our result provides a new area law which improves upon prior work, in terms of the scaling with qudit dimension and spectral gap. In addition, for any bipartition of the grid into a rectangular region $A$ and its complement, we show that the entanglement entropy is upper bounded as $\tilde{O}(|\partial A|^{5/3})$ where $\partial A$ is the boundary of $A$. This represents the first subvolume bound on entanglement in frustration-free 2D systems. In contrast with previous work, our bounds depend on the local (rather than global) spectral gap of the Hamiltonian. We prove our results using a known method which bounds the entanglement entropy of the ground state in terms of certain properties of an approximate ground state projector (AGSP). To this end, we construct a new AGSP which is based on a robust polynomial approximation of the AND function and we show that it achieves an improved trade-off between approximation error and entanglement.

Microscopic insights of magnetism in Sm2NiMnO6 double perovskite

The functional characteristics of double perovskites with unique ferromagnetic-insulator ground state have been controversial due to the unavoidable presence of anti-site disorders (ASDs). Here, we aim to investigate the origin of magnetic ordering on local and global scales in Sm$_{2}$NiMnO$_{6}$ (SNMO) double perovskite system. Different calcination routes are exploited to generate different cation arrangements in SNMO and the corresponding magnetic configurations are examined using the high energy (E $ \sim $0.3 eV) `hot neutrons', which has helped to overcome Sm absorption as well as to record total (Bragg's+diffuse) scattering profiles with high momentum transfer (Q$ _{max} \sim $24 angstrom$ ^{-1} $). We have observed that the Ni-Mn sublattice adopts long range collinear ferromagnetic $ F_{x}F_{z} $ structure with commensurate $k$=(0, 0, 0) propagation vector, below ordering temperature T $ \lesssim $ 160 K, irrespective of variable ASD concentrations. In addition, the signatures indicating the antiparallel polarization of Sm paramagnetic moments with respect to Ni-Mn network, are noticed in the vicinity of anomalous magnetic transitions at T $ \lesssim $ 35 K. The real space pair distribution function calculations have provided a direct visualization of ASDs by means of broadening in Ni/Mn-Mn/Ni linkage. Employing the Reverse Monte Carlo approach on diffuse magnetic scattering profiles, we have observed the negative spin-spin correlation function which suggests the Ni-Ni antiferromagnetic exchange interactions ranging up to first nearest neighbor distance. These results confirm that the existence of ASDs in cation ordered host matrix leads to competing ferromagnetic-antiferromagnetic phases in a broad temperature range, which quantitatively governs the temperature dependent bulk magnetic observables of SNMO system.

The Pursuit of Uniqueness: Extending Valiant-Vazirani Theorem to the Probabilistic and Quantum Settings

Valiant-Vazirani showed in 1985 \cite{VV85} that solving NP with the promise that "yes" instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions).We are interested in extending this result to the quantum setting. We prove extensions to the classes Merlin-Arthur MA and Quantum-Classical-Merlin-Arthur QCMA \cite{AN02}. Our results have implications for the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation (to within polynomial accuracy) of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard, under randomized reductions. This is in stark contrast to the case of constant gapped 1-D Hamiltonians, which is in NP \cite{Has07}. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian that allows efficient calculation of expectation values.Finally, we discuss a few of the obstacles to the establishment of an analogous result to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random projections fail to provide a polynomial gap between two witnesses.

Insights into the anisotropic spin- S Kitaev chain

Recently there has been a renewed interest in properties of the higher-spin Kitaev models, especially their low-dimensional analogues with additional interactions. These quasi-1D systems exhibit rich phase diagrams with symmetry-protected topological phases, Luttinger liquids, hidden order, and higher-rank magnetism. However, the nature of the pure spin-$S$ Kitaev chains are not yet fully understood. Earlier works found a unique ground state with short-ranged correlations for $S = 1$, and an intriguing double-peak structure in the heat capacity associated with an entropy plateau. To understand the low-energy excitations and thermodynamics for general $S$ we study the anisotropic spin-$S$ Kitaev chain. Starting from the dimerized limit we derive an effective low-energy Hamiltonian at finite anisotropy. For half-integer spins we find a trivial effective model, reflecting a non-local symmetry protecting the degeneracy, while for integer $S$ we find interactions among the flux degrees of freedom that select a unique ground state. The effective model for integer spins is used to predict the low-energy excitations and thermodynamics, and we make a comparison with the semiclassical limit through linear spin wave theory. Finally, we speculate on the nature of the isotropic limit.

Exact eigenstates of extended SU(N) Hubbard models: Generalization of η -pairing states with N -particle off-diagonal long-range order

We consider $N$-particle generalizations of $\eta$-pairing states in a chain of $N$-component fermions and show that these states are exact (high-energy) eigenstates of an extended SU($N$) Hubbard model. We compute the singlet correlation function of the states and find that its behavior is qualitatively different for even and odd $N$. When $N$ is even, these states exhibit off-diagonal long-range order in $N$-particle reduced density matrix. On the other hand, when $N$ is odd, the correlations decay exponentially with distance in the bulk, but end-to-end correlations do not vanish in the thermodynamic limit. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.

Spin-Polarized Nematic Order, Quantum Valley Hall States, and Field-Tunable Topological Transitions in Twisted Multilayer Graphene Systems.

We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin-polarized, C_{3z}-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin-polarized, nematic insulator states are in the quantum valley Hall (QVH) phase by virtue of the nontrivial band topology of the systems. The spin-polarized insulator state is quasidegenerate with the valley polarized state if only the dominant intravalley Coulomb interaction is included. Such quasidegeneracy can be split by atomic on-site interactions such that the spin-polarized, nematic state become the unique ground state. Such a scenario applies to various twisted multilayer graphene systems at 1/2 filling, thus can be considered as a universal mechanism. Moreover, under vertical magnetic fields, the orbital Zeeman splittings and the field-induced change of charge density in twisted multilayer graphene systems would compete with the atomic Hubbard interactions, which can drive transitions from spin-polarized zero-Chern-number states to valley-polarized QAH states with small onset magnetic fields.

Magnonic superradiant phase transition

In the superradiant phase transition (SRPT), coherent light and matter fields are expected to appear spontaneously in a coupled light–matter system in thermal equilibrium. However, such an equilibrium SRPT is forbidden in the case of charge-based light–matter coupling, known as no-go theorems. Here, we show that the low-temperature phase transition of ErFeO3 at a critical temperature of approximately 4 K is an equilibrium SRPT achieved through coupling between Fe3+ magnons and Er3+ spins. By verifying the efficacy of our spin model using realistic parameters evaluated via terahertz magnetospectroscopy and magnetization experiments, we demonstrate that the cooperative, ultrastrong magnon–spin coupling causes the phase transition. In contrast to prior studies on laser-driven non-equilibrium SRPTs in atomic systems, the magnonic SRPT in ErFeO3 occurs in thermal equilibrium in accordance with the originally envisioned SRPT, thereby yielding a unique ground state of a hybrid system in the ultrastrong coupling regime.

Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk

AbstractWe prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.

Duality approach to quantum annealing of the 3-variable exclusive-or satisfiability problem (3-XORSAT)

Classical models with complex energy landscapes represent a perspective avenue for the near-term application of quantum simulators. Until now, many theoretical works studied the performance of quantum algorithms for models with a unique ground state. However, when the classical problem is in a so-called clustering phase, the ground state manifold is highly degenerate. As an example, we consider a 3-XORSAT model defined on simple hypergraphs. The degeneracy of classical ground state manifold translates into the emergence of an extensive number of $Z_2$ symmetries, which remain intact even in the presence of a quantum transverse magnetic field. We establish a general duality approach that restricts the quantum problem to a given sector of conserved $Z_2$ charges and use it to study how the outcome of the quantum adiabatic algorithm depends on the hypergraph geometry. We show that the tree hypergraph which corresponds to a classically solvable instance of the 3-XORSAT problem features a constant gap, whereas the closed hypergraph encounters a second-order phase transition with a gap vanishing as a power-law in the problem size. The duality developed in this work provides a practical tool for studies of quantum models with classically degenerate energy manifold and reveals potential connections between glasses and gauge theories.

Local uniqueness of ground states for rotating bose-einstein condensates with attractive interactions

We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap $V(x)$ rotating at the velocity $\Omega $. It is known that there exist a critical rotational velocity $0<\Omega ^*:=\Omega^*(V)\leq \infty$ and a critical number $0<a^*<\infty$ such that for any rotational velocity $0\le \Omega <\Omega ^*$, ground states exist if and only if the coupling constant $a$ satisfies $a<a^*$. For a general class of traps $V(x)$, which may not be symmetric, we prove in this paper that up to a constant phase, there exists a unique ground state as $a\nearrow a^*$, where $\Omega\in(0,\Omega^*)$ is fixed. This result extends essentially our recent uniqueness result, where only the radially symmetric traps $V(x)$ could be handled with.

Mott-insulator-like Bose-Einstein condensation in a tight-binding system of interacting bosons with a flat band

We propose a new class of tight-binding systems of interacting bosons with a flat band, which are exactly solvable in the sense that one can explicitly write down the unique ground state. The ground state is expressed in terms of local creation operators, and apparently resembles that of a Mott insulator. Based on an exact representation in terms of a classical loop-gas model, we conjecture that the ground state may exhibit quasi Bose-Einstein condensation (BEC) or genuine BEC in dimensions two and three or higher, respectively, still keeping Mott insulator-like character. Our Monte Carlo simulation of the loop-gas model strongly supports this conjecture, i.e., the ground state undergoes a Kosterlitz-Thouless transition and exhibits quasi BEC in two dimensions.

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110).

We present results for the electronic and magnetic structure of Mn and Fe clusters on Nb(110) surface, focusing on building blocks of atomic chains as possible realizations of topological superconductivity. The magnetic ground states of the atomic dimers and most of the monatomic chains are determined by the nearest-neighbor isotropic interaction. To gain physical insight, the dependence on the crystallographic direction as well as on the atomic coordination number is analyzed via an orbital decomposition of this isotropic interaction based on the spin-cluster expansion and the difference in the local density of states between ferromagnetic and antiferromagnetic configurations. A spin-spiral ground state is obtained for Fe chains along the [] direction as a consequence of the frustration of the isotropic interactions. Here, a flat spin-spiral dispersion relation is identified, which can stabilize spin spirals with various wave vectors together with the magnetic anisotropy. This may lead to the observation of spin spirals of different wave vectors and chiralities in longer chains instead of a unique ground state.

Lattice protein design using Bayesian learning.

Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a double loop: A loop for amino acid sequence changes and a loop for an exhaustive conformational search for each amino acid sequence. Herein, we propose a novel statistical mechanical design method using Bayesian learning, which can design lattice proteins without the exhaustive conformational search. We consider a thermodynamic hypothesis of the evolution of proteins and apply it to the prior distribution of amino acid sequences. Furthermore, we take the water effect into account in view of the grand canonical picture. As a result, on applying the 2D lattice hydrophobic-polar (HP) model, our design method successfully finds an amino acid sequence for which the target conformation has a unique ground state. However, the performance was not as good for the 3D lattice HP models compared to the 2D models. The performance of the 3D model improves on using a 20-letter lattice proteins. Furthermore, we find a strong linearity between the chemical potential of water and the number of surface residues, thereby revealing the relationship between protein structure and the effect of water molecules. The advantage of our method is that it greatly reduces computation time, because it does not require long calculations for the partition function corresponding to an exhaustive conformational search. As our method uses a general form of Bayesian learning and statistical mechanics and is not limited to lattice proteins, the results presented here elucidate some heuristics used successfully in previous protein design methods.

A $${{\mathbb {Z}}}_2$$-index of Symmetry Protected Topological Phases with Reflection Symmetry for Quantum Spin Chains

For the classification of SPT phases, defining an index is a central problem. In the famous paper (Pollmann et al. Phys Rev B 81:064439, 2010), Pollmann, Tuner, Berg, and Oshikawa introduced $${{\mathbb {Z}}}_2$$ -indices for injective matrix products states which have either $${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$ dihedral group (of $$\pi $$ -rotations about x, y, and z-axes) symmetry, time-reversal symmetry, or reflection symmetry. The first two are on-site symmetries. In Ogata in A $${\mathbb {Z}}_2$$ -index of symmetry protected topological phases with time reversal symmetry for quantum spin chains. arXiv:1810.01045 , an index for on-site symmetries, which generalizes the index in Pollmann et al. (2010), was introduced for general unique gapped ground state phases in quantum spin chains. It was proved that the index is an invariant of the $$C^1$$ -classification of SPT phases. The index for the reflection symmetry, which is not an on-site symmetry, was left as an open question. In this paper, we introduce a $${{\mathbb {Z}}}_2$$ -index for the reflection symmetric unique gapped ground state phases, and complete the generalization problem of index by Pollmann et al. We also show that the index is an invariant of the $$C^1$$ -classification.

Single-layer polymeric tetraoxa[8]circulene modified by s-block metals: toward stable spin qubits and novel superconductors.

Tunable electronic properties of low-dimensional materials have been the object of extensive research, as such properties are highly desirable in order to provide flexibility in the design and optimization of functional devices. In this study, we account for the fact that such properties can be tuned by embedding diverse metal atoms and theoretically study a series of new organometallic porous sheets based on two-dimensional tetraoxa[8]circulene (TOC) polymers doped with alkali or alkaline-earth metals. The results reveal that the metal-decorated sheets change their electronic structure from semiconducting to metallic behaviour due to n-doping. Complete active space self-consistent field (CASSCF) calculations reveal a unique open-shell singlet ground state in the TOC-Ca complex, which is formed by two closed-shell species. Moreover, Ca becomes a doublet state, which is promising for magnetic quantum bit applications due to the long spin coherence time. Ca-doped TOC also demonstrates a high density of states in the vicinity of the Fermi level and induced superconductivity. Using the ab initio Eliashberg formalism, we find that the TOC-Ca polymers are phonon-mediated superconductors with a critical temperature TC = 14.5 K, which is within the range of typical carbon based superconducting materials. Therefore, combining the proved superconductivity and the long spin lifetime in doublet Ca, such materials could be an ideal platform for the realization of quantum bits.

An Extension of the Cell-Construction Method for the Flat-Band Ferromagnetism

We present an extension of the cell-construction method for the flat-band ferromagnetism. In a rather general setting, we construct Hubbard models with highly degenerate single-electron ground states and obtain a formal representation of these single-electron ground states. By our version of the cell-construction method, various types of flat-band Hubbard models, including the one on line graphs, can be designed and shown to have the unique ferromagnetic ground states when the electron number is equal to the degeneracy of the single-electron ground states.