On the valence bond solid in the presence of Dzyaloshinskii-Moriya interaction

We examine the stability of the valence bond solid (VBS) phase against the Dzyaloshinskii-Moriya (DM) interaction in the bipartite lattice. We consider the VBS states in the AKLT model as well as the one in the Sandvik model in the 4×L lattice. We found that the VBS is very stable against the DM interaction qin the AKLT model. There is no quantum phase transition in the AKLT+DM case. However, the VBS spin gap closes in the Sandvik model due to the DM interaction.     

Valence bond entanglement entropy

We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase.     

Optical Bragg,atomic Bragg and cavity QED detections of quantum phases and excitation spectra of ultracold atoms in bipartite and frustrated optical lattices

Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frustrated optical lattices. The physically measurable quantities of the three experiments are the light scattering cross sections, the atom scattered clouds and the cavity leaking photons respectively. We show that the two photon Raman transition processes in the three detection methods not only couple to the density order parameter, but also the valence bond order parameter due to the hopping of the bosons on the lattice. This valence bond order coupling is very sensitive to any superfluid order or any valence bond (VB) order in the quantum phases to be probed. These quantum phases include not only the well-known superfluid and Mott insulating phases, but also other important phases such as various kinds of charge density waves (CDW), valence bond solids (VBS), and CDW-VBS phases with both CDW and VBS orders unique to frustrated lattices, and also various kinds of supersolids. We analyze respectively the experimental conditions of the three detection methods to probe these various quantum phases and their corresponding excitation spectra. We also address the effects of a finite temperature and a harmonic trap. We contrast the three scattering methods with recent in situ measurements inside a harmonic trap and argue that the two kinds of measurements are complementary to each other. The combination of both kinds of detection methods could be used to match the combination of Scanning tunneling microscopy (STM), the Angle Resolved Photo Emission spectroscopy (ARPES) and neutron scattering in condensed matter systems, therefore achieve the putative goals of quantum simulations     

Product Vacua with Boundary States and the Classification of Gapped Phases

We address the question of the classification of gapped ground states in one dimension that cannot be distinguished by a local order parameter. We introduce a family of quantum spin systems on the one-dimensional chain that have a unique gapped ground state in the thermodynamic limit that is a simple product state, but which on the left and right half-infinite chains have additional zero energy edge states. The models, which we call Product Vacua with Boundary States, form phases that depend only on two integers corresponding to the number of edge states at each boundary. They can serve as representatives of equivalence classes of such gapped ground states phases and we show how the AKLT model and its SO(2J + 1)-invariant generalizations fit into this classification.     

Valence-bond states: Link models

An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known anti-ferromagnetic Mott–Hubbard insulators is given by means of the two-point equal-time correlation function obtained (i) numerically from the suggested state and (ii) experimentally from neutron scattering on cuprates in the anti-ferromagnetic insulator phase.     

Variational tests of current order parameters in the Hubbard model

Variational tests are performed for current order parameters as probable sources of the pseudogap normal state of cuprates. The calculations are carried out based on the states with correlations of the valence bond type whose formation can induce in principle both the superconducting order of the d symmetry and current phases. It is shown for the t-t′-U Hubbard models with a large value of U(～8t) and the Hubbard splitting of the conduction band that (1) phases of alternating charge and longitudinal spin currents cannot be realized and (2) transverse spin currents are not compatible with the superconducting order and they could exist against the normal-state background only within a very narrow doping region near the optimal one. This region does not correspond to the region of existence of a pseudogap in cuprates, which refutes the above-mentioned hypothesis of the pseudogap origin. The requirements to the parameters of models for which the consideration of correlations of the valence bond type yields a reasonable phase curve. The existence of current phases in the t-t′-U-V Hubbard models with a strong interaction (V>0.25t) of particles in neighboring sites is predicted when the d-superconductivity is completely suppressed.     

Mott localization nurtures several competing and coexisting orders

Band insulating diamond or metallic mercury differs in a fundamental fashion from materials containing Mott localized electrons. Proliferation of long range orders that compete and sometimes coexist is an important consequence of Mott localization. In this article we focus on how Mott localization creates a rich phase diagram and new physics. A projected nature of the low energy Hilbert space, as opposed to a Fermi gas like Hilbert space, underlies this. Spin, orbital and charge degree of freedom gain independence, but get quantum entangled among themselves and create novel phases. We focus on spin-half single orbital systems. Mott localization encourages entanglement of spin pairs via valence bond formation. We relate valence bond dynamics to emergent gauge fields. Emergent gauge fields in turn nurture and encourage a variety of orders, including topological orders: antiferromagnetism, spin liquids, charge, spin stripes, chiral order and robust superconducting order.     

d-Wave resonating valence bond states of fermionic atoms in optical lattices

We study controlled generation and measurement of superfluid d-wave resonating valence bond (RVB) states of fermionic atoms in 2D optical lattices. Starting from loading spatial and spin patterns of atoms in optical superlattices as pure quantum states from a Fermi gas, we adiabatically transform this state to an RVB state by a change of the lattice parameters. Results of exact time-dependent numerical studies for ladders systems are presented, suggesting generation of RVB states on a time scale smaller than typical experimental decoherence times.     

Dynamical signatures of the one-dimensional deconfined quantum critical point

We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points (DQCPs) in an S = 1/2 spin chain using the time evolution of infinite matrix product states. The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs. The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs. Furthermore, we find an effective spin-charge separation at the DQCP between the ferromagnetic (FM) and valence bond solid (VBS) phases, and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases. Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.     

Semiclassical regime of Regge calculus and spin foams

Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine—as expected from the semiclassical limit of spin foam models—then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.     

Giant paramagnetism in Li-doped Mo-S nanostructures

Magnetic measurements of Li-doped MoS_2−y nanostructures show a peculiarly large T-independent paramagnetic signal, which cannot be understood in terms of either Curie- or Pauli paramagnetism, or—for that matter—in terms of any simple spin-correlated state, such as antiferromagnetism or superparamagnetic spin clustering. This behaviour appears to be a result of a near-ideal one-dimensional (1D) strongly correlated state, due to the extraordinarily weak inherent coupling between 1D subunits (nanotubes or nanowires), which is an order of magnitude weaker even than in carbon nanotube ropes. In spite of clear evidence for strong electronic correlations from a giant paramagnetic susceptibility, no transition to an ordered state is observed down to very low temperatures and the system appears to be stabilised in a paramagnetic state by fluctuations characteristic of 1D systems. Down to 2 K there is no evidence of a low-temperature quantum critical point.     

Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strong enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.     

Rydberg quantum computation with nuclear spins in two-electron neutral atoms

Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states |0〉 and |1〉 are excited to Rydberg states |r〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state |1〉 can be fully excited to the Rydberg state while |0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.     

Ground States of Quantum Antiferromagnets in Two Dimensions

We explore the ground states and quantum phase transitions of two-dimensional, spin S=1/2, antiferromagnets by generalizing lattice models and duality transforms introduced by Sachdev and Jalabert (1990, Mod. Phys. Lett. B4, 1043). The minimal model for square lattice antiferromagnets is a lattice discretization of the quantum nonlinear sigma model, along with Berry phases which impose quantization of spin. With full SU(2) spin rotation invariance, we find a magnetically ordered ground state with Néel order at weak coupling and a confining paramagnetic ground state with bond charge (e.g., spin Peierls) order at strong coupling. We study the mechanisms by which these two states are connected in intermediate coupling. We extend the minimal model to study different routes to fractionalization and deconfinement in the ground state, and also generalize it to cases with a uniaxial anisotropy (the spin symmetry groups is then U(1)). For the latter systems, fractionalization can appear by the pairing of vortices in the staggered spin order in the easy-plane; however, we argue that this route does not survive the restoration of SU(2) spin symmetry. For SU(2) invariant systems we study a separate route to fractionalization associated with the Higgs phase of a complex boson measuring noncollinear, spiral spin correlations: we present phase diagrams displaying competition between magnetic order, bond charge order, and fractionalization, and discuss the nature of the quantum transitions between the various states. A strong check on our methods is provided by their application to S=1/2 frustrated antiferromagnets in one dimension: here, our results are in complete accord with those obtained by bosonization and by the solution of integrable models.     

Two-dimensional lattice gauge theories with superconducting quantum circuits

A quantum simulator of U(1)$U\left(1\right)$ lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.     

Emergence of superconductivity, valence bond order, and Mott insulators in Pd[(dmit)2] based organic salts

The EtMe(3)P and EtMe(3)Sb triangular organic salts are distinguished from other Pd[(dmit)(2)] based salts, as they display valence bond and no long-range order, respectively. Under pressure, a superconducting phase is revealed in EtMe(3)P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperature phase diagram manifests a remarkable resemblance to the phase diagram of the EtMe(3)P salt, where the reentrant transition of insulator-metal-insulator type can be explained by an entropy difference between the metal and U(1) spin liquid. We predict different temperature dependence of the specific heat between the spin liquid and metal.     

Dual vortex theory of doped Mott insulators

We present a general framework for describing the quantum phases obtained by doping paramagnetic Mott insulators on the square lattice. The undoped insulators are efficiently characterized by the projective transformations of various fields under the square lattice space group (the PSG). We show that the PSG also imposes powerful constraints on the doped system, and on the effective action for the vortex and Bogoliubov quasiparticle excitations of superconducting states. This action can also be extended across transitions to supersolid or insulating states at non-zero doping. For the case of a valence bond solid (VBS) insulator, we show that the doped system has the same PSG as that of elementary bosons with density equal to the density of electron Cooper pairs. We also discuss aspects of the action for a d-wave superconductor obtained by doping a “staggered-flux” spin liquid state.     

Thermodynamics of a dilute XX chain in a field

Gapless phases in ground states of low-dimensional quantum spin systems are rather ubiquitous. Their peculiarity is a remarkable sensitivity to external perturbations due to permanent criticality of such phases manifested by a slow (power-low) decay of pair correlations and the divergence of the corresponding susceptibility. A strong influence of various defects on the properties of the system in such a phase can then be expected. Here, we consider the influence of vacancies on the thermodynamics of the simplest quantum model with a gapless phase, the isotropic spin-1/2 XX chain. The existence of the exact solution of this model gives a unique opportunity to describe in detail the dramatic effect of dilution on the gapless phase—the appearance of an infinite series of quantum phase transitions resulting from level crossing under the variation of a longitudinal magnetic field. We calculate the jumps in the field dependences of the ground-state longitudinal magnetization, susceptibility, entropy, and specific heat appearing at these transitions and show that they result in a highly nonlinear temperature dependence of these parameters at low T. Also, the effect of enhancement of the magnetization and longitudinal correlations in the dilute chain is established. The changes of the pair spin correlators under dilution are also analyzed. The universality of the mechanism of the quantum transition generation suggests that similar effects of dilution can also be expected in gapless phases of other low-dimensional quantum spin systems.     

Controlling and detecting spin correlations of ultracold atoms in optical lattices

We report on the controlled creation of a valence bond state of delocalized effective-spin singlet and triplet dimers by means of a bichromatic optical superlattice. We demonstrate a coherent coupling between the singlet and triplet states and show how the superlattice can be employed to measure the singlet-fraction employing a spin-blockade effect. Our method provides a reliable way to detect and control nearest-neighbor spin correlations in many-body systems of ultracold atoms. Being able to measure these correlations is an important ingredient in studying quantum magnetism in optical lattices. We furthermore employ a SWAP operation between atoms which are part of different triplets, thus effectively increasing their bond-length. Such a SWAP operation provides an important step towards the massively parallel creation of a multiparticle entangled state in the lattice.     

一维量子子自自旋链中拓扑有序态的物理描述

一维量子多体系统是凝聚态物理学中的重要研究方向之一,其中的新奇量子物态则是重要的研究课题。本文我们首先简要回顾一维量子整数自旋链体系的相关研究背景,然后提出一类SO(n)对称的严格可解量子自旋链模型及其矩阵乘积基态。当奇数n≥3时,体系的基态为Haldane相。利用这类态中隐藏的稀薄反铁磁序,我们找到了刻画这类态的非局域弦序参量,并在隐藏拓扑对称性的统一框架下解释了稀薄反铁磁序以及边缘态等奇特现象的起源。当偶数n≥4时,体系的基态为二聚化态。这些态属于破缺平移对称性的非Haldane相,但同样具有隐藏的反铁磁序。通过这些严格解的研究,我们还得到了一维SO(n)对称的双线性–双二次模型的基态相图,并发现在n≥5时,一维SO(n)对称的反铁磁海森堡模型的基态处于二聚化相中。基于以上这些结果,我们推广构造了一维平移不变且包含李群G对称性的Valence BondState(VBS)态,并利用其矩阵乘积表示讨论了对应哈密顿量的构造方法。对于自旋为S的量子整数自旋链,我们研究了两类具有不同拓扑属性的VBS类,前一类VBS态的边缘态处于SU(2)自旋J的不可约表示,后一类VBS态的边缘态为SO(2S+1)旋量。在前一类态中,我们以自旋为1的费米型VBS态为例构造了对应的哈密顿量。对后一类态,我们证明了它们等价于SO(2S+1)矩阵乘积态,从而揭示了呈展对称性的起源和边缘态的性质。我们还推广了SO(5)对称的玻色型和费米型VBS态,并探讨了它们的拓扑刻画方式。