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We investigate the role of the permutationally invariant part of the density matrix (PIDM) in capturing the properties of the ground state of the system during a quantum phase transition. In the context of quantum state tomography, PIDM is known to be obtainable with only a low number of measurement settings, namely $\mathcal{O}(L^2)$, where $L$ is the system size. Considering the transverse-field Ising chain as an example, we compute the second-order R\'enyi entropy of PIDM for the ground state by using the density matrix renormalization group algorithm. In the ferromagnetic case, the ground state is permutationally invariant both in the limits of zero and infinite field, leading to vanishing R\'enyi entropy of PIDM. The latter exhibits a broad peak as a function of the transverse field around the quantum critical point, which gets more pronounced for larger system size. In the antiferromagnetic case, the peak structure disappears and the R\'enyi entropy diverges like $\mathcal{O}(L)$ in the whole field range of the ordered phase. We discuss the cause of these behaviors of the R\'enyi entropy of PIDM, examining the possible application of this experimentally tractable quantity to the analysis of phase transition phenomena.

An advanced cooling scheme, incorporating entropy engineering, is vital for isolated artificial quantum systems designed to emulate the low-temperature physics of strongly correlated electron systems (SCESs). This study theoretically demonstrates a cooling method employing multi-component Fermi gases with SU($\mathcal{N}$)-symmetric interactions, focusing on the case of $^{173}$Yb atoms in a two-dimensional optical lattice. Adiabatically introducing a nonuniform state-selective laser gives rise to two distinct subsystems: a central low-temperature region, exclusively composed of two specific spin components, acts as a quantum simulator for SCESs, while the surrounding $\mathcal{N}$-component mixture retains a significant portion of the entropy of the system. The SU($\mathcal{N}$)-symmetric interactions ensure that the total particle numbers for each component become good quantum numbers, creating a sharp boundary for the two-component region. The cooling efficiency is assessed through extensive finite-temperature Lanczos calculations. The results lay the foundation for quantum simulations of two-dimensional systems of Hubbard or Heisenberg type, offering crucial insights into intriguing low-temperature phenomena in condensed-matter physics., Comment: 6 pages, 3 figures

Quantum many-body systems are expected to relax to a thermal state over time, with some exceptions such as systems with atypical eigenstates. In this study, we investigate the effect of the existence of spatially localized eigenstates on the relaxation dynamics of interacting bosons loaded into a one-dimensional sawtooth lattice, which exhibits a flat band in the single-particle spectrum by tuning the hopping rates. Using the time-evolving block decimation algorithm, we simulate the time evolution of the local density profile based on the Bose-Hubbard model with different initial conditions. Our results show the presence of the flat band leads to a significant slowing down of relaxation for weak interactions. Even for strong interaction, when the initial state includes an isolated localized single-particle eigenstate in the superposition, remnants of the initial bias in the density profile persist for a long time. This particular relaxation dynamics can be tested using ultracold atoms in optical lattices., Comment: 8 pages, 9 figures

According to the AdS/CFT correspondence, certain quantum many-body systems in $d$-dimensions are equivalent to gravitational theories in $(d+1)$-dimensional asymptotically AdS spacetimes. When a massless particle is sent from the AdS boundary to the bulk curved spacetime, it reaches another point of the boundary after a time lag. In the dual quantum system, it should appear as if quasiparticles have been transferred between two separated points. We theoretically demonstrate that this phenomenon, which we call "spacetime-localized response," is actually observed in the dynamics of the one-dimensional transverse-field Ising model near the quantum critical point. This result suggests that, if we can realize a holographic spin system in a laboratory, the experimental probing of the emergent extra-dimension is possible by applying a designed stimulus to a quantum many-body system, which is holographically equivalent to sending a massless particle through the higher-dimensional curved bulk geometry. We also discuss possible experimental realizations using Rydberg atoms in an optical tweezers array., Comment: 10 pages, 6 figures, Ver. 2: matches the PRD published version

We focus on three-component SU(3) Fermi gases loaded into a square optical lattice, with population imbalance between one component and the others. At strong coupling the system is described by the SU(3) Heisenberg model with an external field that couples to the population imbalance. We discuss the ground state at the mean-field level and then analyze the thermal fluctuations with the semi-classical Monte Carlo method. The interplay of interactions, population imbalance and thermal fluctuations gives rise to a phase transition linked to the breaking of an emergent Ising symmetry, despite the absence of frustration. This represents a new scenario of discrete symmetry breaking in low-dimensional systems with continuous symmetries. Possible implementations with cold alkaline-earth(-like) atoms are discussed., Comment: 5 pages, 5 figures

Ba$_3$CoSb$_2$O$_9$ approximates the two-dimensional spin-1/2 triangular-lattice Heisenberg antiferromagnet. This compound displays magnetic-field-induced quantum phase transitions, including the 1/3-magnetization-plateau, but its magnetization processes for the magnetic field $H$ parallel and perpendicular to the $c$ axis are different due to the weak easy-plane anisotropy and the weak interlayer antiferromagnetic exchange interaction. To elucidate how the quantum phase transitions change between these two field directions, we measured the field-angle dependence of the magnetization process in Ba$_3$CoSb$_2$O$_9$ using pulsed high magnetic fields. We compared obtained magnetic field-field angle phase diagram with those obtained by the large-size cluster mean-field method combined with a scaling scheme and the semiclassical theory. We also found a narrow 1/3-magnetization plateau and a high-field transition with a small magnetization jump for $H\,{\parallel}\,c$, not observed in the previous studies., Comment: 8 pages, 7 figures, to appear in Phys. Rev. B

We study the quantum magnetism of the SU(4) Mott insulator in a square optical superlattice, in which atoms with four nuclear-spin components strongly interact with each other, in the presence of an external field that controls the imbalance between the population of two components and that of the other two. This is a natural extension of the physics of spin-dimer materials under strong magnetic field. We apply an extended linear flavor-wave theory based on four-site plaquettes and unveil the ground-state phase diagram and excitation spectra. When the population of the four components is balanced and the plaquesttes are weakly coupled, the ground state is approximately given by the direct product of local SU(4)-singlet states. In high-field, the system reaches a "saturated state" where only two components are present. Our main finding is a nontrivial intermediate phase, which has a checkerboard-like arrangement of the SU(4)-singlet and four-site resonating-valence-bond states., Comment: 5+7 pages, 7+2 figures, to be published in Journal of the Physical Society of Japan

We study the emergence of supersolid Devil's staircases of spin-orbit coupled bosons loaded in optical lattices. We consider two- and three-dimensional systems of pseudo-spin-$1/2$ bosons interacting via local spin-dependent interactions. These interactions together with spin-orbit coupling produce length scales that are commensurate to the lattice spacing. This commensurability leads to Devil's staircases of supersolids, with fractal Hausdorff dimensions, which arise from uniform superfluid phases. We show that umklapp processes are essential for the existence of commensurate supersolids, and that without them the Devil's staircase does not exist. Lastly, we emphasize the generality of our results, suggest experiments that can unveil these unusual predictions, and discuss potential applications to the case of $^{87}$Rb., Comment: 6 pages, 4 figures

We theoretically study dynamical formation of a quantum droplet in a two-component Bose-Hubbard system with an external trap potential. Specifically, the superfluid in the central region surrounded by the Mott insulator with double filling forms a quantum droplet, which is self-bound thanks to the discontinuous nature of the quantum phase transition between the two phases. We show how to induce the characteristic behavior of the droplet through the control of the trap potential by using the time-dependent Gutzwiller simulations in a two-dimensional system. The static and dynamical properties of the droplet can be described qualitatively by the effective Ginzburg-Landau field theory with cubic-quintic nonlinearities, where the attractive cubic nonlinearlity emerges although all the bare interparticle interactions are repulsive., Comment: 9 pages, 5 figures

In solid materials, the parameters relevant to quantum effects, such as the spin quantum number, are basically determined and fixed at the chemical synthesis, which makes it challenging to control the amount of quantum correlations. We propose and demonstrate a method for active control of the classical-quantum crossover in magnetic insulators by applying external pressure. As a concrete example, we perform high-field, high-pressure measurements on CsCuCl$_3$, which has the structure of weakly-coupled spin chains. The magnetization process experiences a continuous evolution from the semi-classical realm to the highly-quantum regime with increasing pressure. Based on the idea of "squashing" the spin chains onto a plane, we characterize the change in the quantum correlations by the change in the value of the local spin quantum number of an effective two-dimensional model. This opens a way to access the tunable classical-quantum crossover of two-dimensional spin systems by using alternative systems of coupled-chain compounds., Comment: 11 + 3 pages, 10 + 2 figures

We study the quantum and thermal phase transition phenomena of the SU(3) Heisenberg model on triangular lattice in the presence of magnetic fields. Performing a scaling analysis on large-size cluster mean-field calculations endowed with a density-matrix-renormalization-group solver, we reveal the quantum phases selected by quantum fluctuations from the massively degenerate classical ground-state manifold. The magnetization process up to saturation reflects three different magnetic phases. The low- and high-field phases have strong nematic nature, and especially the latter is found only via a nontrivial reconstruction of symmetry generators from the standard spin and quadrupolar description. We also perform a semiclassical Monte Carlo simulations to show that thermal fluctuations prefer the same three phases as well. Moreover, we find that exotic topological phase transitions driven by the binding-unbinding of fractional (half-)vortices take place, due to the nematicity of the low- and high-field phases. Possible experimental realization with alkaline-earth-like cold atoms is also discussed., Comment: 6+6 pages, 4+4 figures

Quantum antiferromagnets with geometrical frustration exhibit rich many-body physics but are hard to simulate by means of classical computers. Although quantum-simulation studies for analyzing such systems are thus desirable, they are still limited to high temperature regions, where interesting quantum effects are smeared out. Here, we propose a feasible protocol to perform analog quantum simulation of frustrated antiferromagnetism with strong quantum fluctuations by using ultracold Bose gases in optical lattices at negative absolute temperatures. Specifically, we show from numerical simulations that the time evolution of a negative-temperature state subjected to a slow sweep of the hopping energy simulates quantum phase transitions of a frustrated Bose-Hubbard model with sign-inverted hoppings. Moreover, we quantitatively predict the phase boundary between the frustrated superfluid and Mott-insulator phases for triangular lattices with hopping anisotropy, which serves as a benchmark for quantum simulation., Comment: 12 pages, 9 figures

Nontrivial magnetic orders in the inverse-perovskite manganese nitrides are theoretically studied by constructing a classical spin model describing the magnetic anisotropy and frustrated exchange interactions inherent in specific crystal and electronic structures of these materials. With a replica-exchange Monte-Carlo technique, a theoretical analysis of this model reproduces the experimentally observed triangular \Gamma^{5g} and \Gamma^{4g} spin ordered patterns and the systematic evolution of magnetic orders. Our work solves a 40-year-old problem of nontrivial magnetism for the inverse-perovskite manganese nitrides and provides a firm basis for clarifying the magnetism-driven negative thermal expansion phenomenon discovered in this class of materials., Comment: 5 pages, 5 figures

Magnetic excitations of the effective spin $S$=1/2 dimerized magnet Ba$_2$CoSi$_2$O$_6$Cl$_2$ have been probed directly via inelastic neutron scattering experiments at temperatures down to 4 K. We observed five types of excitation at 4.8, 5.8, 6.6, 11.4, and 14.0 meV, which are all dispersionless within the resolution limits. The scattering intensities of the three low-lying excitations were found to exhibit different $Q$-dependences. Detailed analysis has demonstrated that Ba$_2$CoSi$_2$O$_6$Cl$_2$ is a two-dimensional spin dimer system described only by a single dimer site, where the triplet excitations are localized owing to the almost perfect frustration of the interdimer exchange interactions and the undimerized spins, even in small concentration, make an essential contribution to the excitation spectrum., Comment: 6 pages, 3 figures, accepted for publication in Phys. Rev. Lett

Quantum simulators based on cold atomic gases can provide an ideal platform to study the microscopic mechanisms behind intriguing properties of solid materials and further explore novel exotic phenomena inaccessible by chemical synthesis. Here we propose and theoretically analyze a coherently coupled binary mixture of Fermi atoms in a triangular optical lattice as a promising realization of synthetic frustrated antiferromagnets. We perform a cluster mean-field plus scaling analysis to show that the ground state exhibits several nontrivial magnetic phases and a novel spin reorientation transition caused by the quantum order-by-disorder mechanism. Moreover, we find from Monte Carlo simulations that thermal fluctuations induce an unexpected coexistence of Berezinskii-Kosterlitz-Thouless physics and long-range order in different correlators. These predictions, besides being relevant to present and future experiments on triangular antiferromagnetic materials, can be tested in the laboratory with the combination of the currently available techniques for cold atoms., Comment: 9 pages, 7 figures

A massive Goldstone (MG) mode, often referred to as a Higgs amplitude mode, is a collective excitation that arises in a system involving spontaneous breaking of a continuous symmetry, along with a gapless Nambu-Goldstone mode. It has been known in the previous studies that a pure amplitude MG mode emerges in superconductors if the dispersion of fermions exhibits the particle-hole (p-h) symmetry. However, clear understanding of the relation between the symmetry of the Hamiltonian and the MG modes has not been reached. Here we reveal the fundamental connection between the discrete symmetry of the Hamiltonian and the emergence of pure amplitude MG modes. To this end, we introduce nontrivial charge-conjugation ($\mathcal C$), parity ($\mathcal P$), and time-reversal ($\mathcal T$) operations that involve the swapping of pairs of wave vectors symmetrical with respect to the Fermi surface. The product of $\mathcal{CPT}$ (or its permutations) represents an exact symmetry analogous to the CPT theorem in the relativistic field theory. It is shown that a fermionic Hamiltonian with a p-h symmetric dispersion exhibits the discrete symmetries under $\mathcal C$, $\mathcal P$, $\mathcal T$, and $\mathcal{CPT}$. We find that in the superconducting ground state, $\mathcal T$ and $\mathcal P$ are spontaneously broken simultaneously with the U(1) symmetry. Moreover, we rigorously show that amplitude and phase fluctuations of the gap function are uncoupled due to the unbroken $\mathcal C$. In the normal phase, the MG and NG modes become degenerate, and they have opposite parity under $\mathcal T$. Therefore, we conclude that the lifting of the degeneracy in the superconducting phase and the resulting emergence of the pure amplitude MG mode can be identified as a consequence of the the spontaneous breaking of $\mathcal T$ symmetry but not of $\mathcal P$ or U(1)., Comment: 11 pages, 5 figures. v2: Sec. VII substantially revised to improve the inaccurate discussions on the restoring of the T symmetry in v1. v3: minor corrections, published version

Ultracold bosons in optical lattices are one of the few systems where bosonic matter is known to exhibit strong correlations. Here we push the frontier of our understanding of interacting bosons in optical lattices by adding synthetic spin-orbit coupling, and show that new kinds of density- and chiral-orders develop. The competition between the optical lattice period and the spin-orbit coupling length -- which can be made comparable in experiments -- along with the spin hybridization induced by a transverse field (i.e., Rabi coupling) and interparticle interactions create a rich variety of quantum phases including uniform, non-uniform and phase-separated superfluids, as well as Mott insulators. The spontaneous symmetry breaking phenomena at the transitions between them are explained by a two-order-parameter Ginzburg-Landau model with multiparticle umklapp processes. Finally, in order to characterize each phase, we calculated their experimentally measurable crystal momentum distributions., Comment: 6+9 pages, 4 figures

Quantum magnetic phases near the magnetic saturation of triangular-lattice antiferromagnets with XXZ anisotropy have been attracting renewed interest since it has been suggested that a nontrivial coplanar phase, called the $\pi$-coplanar or $\Psi$ phase, could be stabilized by quantum effects in a certain range of anisotropy parameter $J/J_z$ besides the well-known 0-coplanar (known also as $V$) and umbrella phases. Recently, Sellmann $et$ $al$. [Phys. Rev. B {\bf 91}, 081104(R) (2015)] claimed that the $\pi$-coplanar phase is absent for $S=1/2$ from an exact-diagonalization analysis in the sector of the Hilbert space with only three down-spins (three magnons). We first reconsider and improve this analysis by taking into account several low-lying eigenvalues and the associated eigenstates as a function of $J/J_z$ and by sensibly increasing the system sizes (up to 1296 spins). A careful identification analysis shows that the lowest eigenstate is a chirally antisymmetric combination of finite-size umbrella states for $J/J_z\gtrsim 2.218$ while it corresponds to a coplanar phase for $J/J_z\lesssim 2.218$. However, we demonstrate that the distinction between 0-coplanar and $\pi$-coplanar phases in the latter region is fundamentally impossible from the symmetry-preserving finite-size calculations with fixed magnon number.} Therefore, we also perform a cluster mean-field plus scaling analysis for small spins $S\leq 3/2$. The obtained results, together with the previous large-$S$ analysis, indicate that the $\pi$-coplanar phase exists for any $S$ except for the classical limit ($S\rightarrow \infty$) and the existence range in $J/J_z$ is largest in the most quantum case of $S=1/2$., Comment: 13 pages, 13 figures