Extrapolating the results of hybrid quantum Monte Carlo simulations to the zero temperature and infinite-chain-length limits, we calculate the ground-state phase diagram of a system of quantum particles on a chain of harmonically coupled, symmetric, quartic double-well potentials. We show that the ground state of this quantum chain depends on two parameters, formed from the ratios of the three natural energy scales in the problem. As a function of these two parameters, the quantum ground state can exhibit either broken symmetry, in which the expectation values of the particle's coordinate are all nonzero (as would be the case for a classical chain), or restored symmetry, in which the expectation values of the particle's coordinate are all zero (as would be the case for a single quantum particle). In addition to the phase diagram as a function of these two parameters, we calculate the ground-state energy, an order parameter related to the average position of the particle, and the susceptibility associated with this order parameter. Further, we present an approximate analytic estimate of the phase diagram and discuss possible physical applications of our results, emphasizing the behavior of hydrogen halides under pressure.
We investigate both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1/2-1-1 chain described by the Hamiltonian $H=\sum_{\ell=1}^{N/4} (J_1\vecs_{4\ell-3}\cdot \vecs_{4\ell-2}+J_2\vecs_{4\ell-2}\cdot\vecS_{4\ell-1}+J_3\vecS_{4\ell-1}\cdot \vecS_{4\ell}+J_2\vecS_{4\ell}\cdot\vecs_{4\ell+1})$, where two
S=1/2 spins ($\vecs_{4\ell-3}$ and $\vecs_{4\ell-2}$) and two S=1 spins ($\vecS_{4\ell-1}$ and $\vecS_{4\ell}$) are arranged alternatively. Inseveral limiting cases of
J1,
J2, and
J3 we apply the Wigner-Eckart theorem and carry out a perturbation calculation to examine the behavior of the massless lines where the energy gap vanishes. Performing a quantum Monte Carlo calculation without global flips at a sufficiently low temperature for the case where
J1=J3=1.0 and
J2>0, we find that the ground state of the present system in this case undergoes a second-order phase transition accompanying the vanishing of the energy gap at $J_2=J_{2c$ with
J2c=0.77±0.01. We also find that the ground states for both $J_2 < J_{2 c$ and $J_2 > J_{2c$ can be understood by means of the valence-bond-solid picture. A quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account is carried out to elucidate the temperature dependences of the specific heat and the magnetic susceptibility. In particular, it is found that the susceptibility per unit cell for
J2=0.77 with
J1=J3=1.0 takes a finite value at absolute zero temperature and that the specific heat per unit cell versus temperature curve for
J2=5.0 with
J1=J3=1.0 has a double peak.
The discrete time path integral Monte Carlo with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action for a single particle in a double-well potential is used to construct the many-particle action. The algorithm is applied to the interacting quantum double-well chain for which the zero-temperature phase diagram is determined. The quantum phase transition is studied via finite-size scaling, and the critical exponents are shown to be compatible with the classical two-dimensional Ising universality class--not only in the order-disorder limit (deep potential wells), but also in the displacive regime (shallow potential wells).
The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.
The density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field
h. The Hamiltonian contains exchange terms involving the intratrimer coupling
J1 (taken as the unit of energy) and the intertrimer coupling
J2, plus the Zeeman interaction for a magnetic field
h along the
z direction. Results for the magnetization per trimer
m are calculated in regimes of positive and negative values of the ratio
J=J2/J1, from which the rich field-induced ground state phase diagram
h versus
J is derived, with the presence of a Luttinger liquid, the 1/3 plateau (
m=1/2), and the one of fully polarized magnetization (
m=3/2). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for
Sz=1 is shown at the previous regimes of
J values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by
1/∣J∣ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound
Pb3Cu3(PO4)4 and estimate the model exchange couplings:
J1=74.8K and
J=0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on
Pb3Cu3(PO4)4 for two excitation modes. The 1/3 plateau closes only at
1/∣J∣=0 with
J<0.
The ability to accurately predict the finite temperature properties and phase diagrams of realistic quantum solids is central to uncovering new phases and engineering materials with novel properties ripe for device applications. Nonetheless, there remain comparatively few many-body techniques capable of elucidating the finite temperature physics of solids from first principles. In this work, we take a significant step toward developing such a technique by generalizing our previous, exact fully ab initio finite temperature Auxiliary Field Quantum Monte Carlo (FT-AFQMC) method to model periodic solids and employing it to uncover the finite temperature physics of periodic hydrogen chains. Our chains’ unit cells consist of 10 hydrogen atoms modeled in a minimal basis, and we sample 5 k-points from the first Brillouin zone to arrive at a supercell consisting of 50 orbitals and 50 electrons. Based upon our calculations of these chains’ many-body energies, free energies, entropies, heat capacities, double and natural occupancies, and charge and spin correlation functions, we outline their metal–insulator and magnetic ordering as a function of both H–H bond distance and temperature. At low temperatures approaching the ground state, we observe both metal–insulator and ferromagnetic–antiferromagnetic crossovers at bond lengths between 0.5 and 0.75 Å. We then demonstrate how this low-temperature ordering evolves into a metallic phase with decreasing magnetic order at higher temperatures. In order to contextualize our results, we compare the features we observe to those previously seen in one-dimensional, half-filled Hubbard models at finite temperature and in ground state hydrogen chains. Interestingly, we identify signatures of the Pomeranchuk effect in hydrogen chains for the first time and show that spin and charge excitations that typically arise at distinct temperatures in the Hubbard model are indistinguishably coupled in these systems. Beyond qualitatively revealing the many-body phase behavior of hydrogen chains in a numerically exact manner without invoking the phaseless approximation, our efforts shed light on the further theoretical developments that will be required to construct the phase diagrams of the more complex transition metal, lanthanide, and actinide solids of longstanding interest to physicists.
The ground-state and thermodynamic properties of quantum mixed-spin chains of 1/2-1/2-1-1 and 3/2-3/2-1-1 are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameter .