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Register a new userBroken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
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Added by
Nikita Astrakhantsev
Publication date
2021
fields
Physics
and research's language is
English
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The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4times 4^3$ and $4 times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin-liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.
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We use the rotation-invariant Greens function method (RGM) and the high-temperature expansion (HTE) to study the thermodynamic properties of the Heisenberg antiferromagnet on the pyrochlore lattice. We discuss the excitation spectra as well as various thermodynamic quantities, such as spin correlations, uniform susceptibility, specific heat and static and dynamical structure factors. For the ground state we present RGM data for arbitrary spin quantum numbers $S$. At finite temperatures we focus on the extreme quantum cases $S=1/2$ and $S=1$. We do not find indications for magnetic long-range order for any value of $S$. We discuss the width of the pinch point in the static structure factor in dependence on temperature and spin quantum number. We compare our data with experimental results for the pyrochlore compound NaCaNi$_2$F$_7$ ($S=1$). Thus, our results for the dynamical structure factor agree well with the experimentally observed features at 3 ldots 8~meV for NaCaNi$_2$F$_7$. We analyze the static structure factor ${S}_{bf q}$ to find regions of maximal ${S}_{bf q}$. The high-temperature series of the ${S}_{bf q}$ provide a fingerprint of weak {it order by disorder} selection of a collinear spin structure, where (classically) the total spin vanishes on each tetrahedron and neighboring tetrahedra are dephased by $pi$.
We give a complete classification of fully symmetric as well as chiral $mathbb{Z}_2$ quantum spin liquids on the pyrochlore lattice using a projective symmetry group analysis of Schwinger boson mean-field states. We find 50 independent ansatze, including the 12 fully symmetric nearest-neighbor $mathbb{Z}_2$ spin liquids that have been classified by Liu et al. [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.075125]. For each class we specify the most general symmetry-allowed mean-field Hamiltonian. Additionally, we test the properties of a subset of the spin liquid ansatze by solving the mean-field equations for the spin-$1/2$ XXZ model near the antiferromagnetic Heisenberg point. We find that the ansatz with the lowest energy at mean-field level is a chiral spin liquid that breaks the screw symmetry of the lattice modulo time reversal symmetry. This state has a different symmetry than the previously studied monopole flux state. Moreover, this chiral spin liquid state has a substantially lower energy than all other symmetric spin liquid states, suggesting that it could be a stable ground state beyond the mean-field approximation employed in this work.
We analyze the problem of how different ground states associated to the same set of the Hamiltonian parameters evolve after a sudden quench. To realize our analysis we define a quantitative approach to the local distinguishability between different ground states of a magnetically ordered phase in terms of the trace distance between the reduced density matrices obtained projecting two ground states in the same subset. Before the quench, regardless the particular choice of the subset, any system in a magnetically ordered phase is characterized by ground states that are locally distinguishable. On the other hand, after the quench, the maximum of the distinguishability shows an exponential decay in time. Hence, in the limit of very large time, all the informations about the particular initial ground state are lost even if the systems are integrable. We prove our claims in the framework of the magnetically ordered phases that characterize both the $XY$ model and $N$-cluster Ising models. The fact that we find similar behavior in models within different classes of symmetry makes us confident about the generality of our results.
We investigate classical Heisenberg spins on the Shastry-Sutherland lattice and under an external magnetic field. A detailed study is carried out both analytically and numerically by means of classical Monte-Carlo simulations. Magnetization pseudo-plateaux are observed around 1/3 of the saturation magnetization for a range of values of the magnetic couplings. We show that the existence of the pseudo-plateau is due to an entropic selection of a particular collinear state. A phase diagram that shows the domains of existence of those pseudo-plateaux in the $(h, T)$ plane is obtained.
We have extended the canonical tree tensor network (TTN) method, which was initially introduced to simulate the zero-temperature properties of quantum lattice models on the Bethe lattice, to finite temperature simulations. By representing the thermal density matrix with a canonicalized tree tensor product operator, we optimize the TTN and accurately evaluate the thermodynamic quantities, including the internal energy, specific heat, and the spontaneous magnetization, etc, at various temperatures. By varying the anisotropic coupling constant $Delta$, we obtain the phase diagram of the spin-1/2 Heisenberg XXZ model on the Bethe lattice, where three kinds of magnetic ordered phases, namely the ferromagnetic, XY and antiferromagnetic ordered phases, are found in low temperatures and separated from the high-$T$ paramagnetic phase by a continuous thermal phase transition at $T_c$. The XY phase is separated from the other two phases by two first-order phase transition lines at the symmetric coupling points $ Delta=pm 1$. We have also carried out a linear spin wave calculation on the Bethe lattice, showing that the low-energy magnetic excitations are always gapped, and find the obtained magnon gaps in very good agreement with those estimated from the TTN simulations. Despite the gapped excitation spectrum, Goldstone-like transverse fluctuation modes, as a manifestation of spontaneous continuous symmetry breaking, are observed in the ordered magnetic phases with $|Delta|le 1$. One remarkable feature there is that the prominent transverse correlation length reaches $xi_c=1/ln{(z-1)}$ for $Tleq T_c$, the maximal value allowed on a $z$-coordinated Bethe lattice.
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