Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model

Abstract

We show that the highly frustrated transverse-field Ising model on the three-dimensional pyrochlore lattice realizes a first-order phase transition without symmetry breaking between the lowfield Coulomb quantum spin liquid and the high-field polarized phase. The quantum phase transition is located quantitively by comparing low-and high-field series expansions. Furthermore, the intriguing properties of the elementary excitations in the polarized phase are investigated. We argue that this model can be achieved experimentally by applying mechanical strain to a classical spin ice material comprised of non-Kramers spins such as Ho2Ti2O7. Taken together with our results, this provides a new experimental platform to study quantum spin liquid physics.The appearance of new collective degrees of freedom in strongly correlated systems is a pervasive theme in physics, exemplified in magnetism by spin liquids -highly correlated states of spins with novel excitations and emergent gauge structures [1,2]. Amongst the most storied examples of the latter are the spin ice pyrochlores, Ho 2 Ti 2 O 7 or Dy 2 Ti 2 O 7 where strong geometric frustration among coupled magnetic moments gives rise to classical spin liquids with defects that behave like magnetic monopoles [3][4][5].Quantum effects are essentially zero in these spin-ice compounds, which are described accurately by classical Ising models -i.e. only the (local) σ z i component of the spins appears in the Hamiltonian. However, theoretically, a quantum version of spin ice is highly desirable. One expects the presence of a so-called Coulomb quantum spin liquid (CQSL) [1,6,7] with gapped electric and magnetic excitations as well as an emergent photon. Quantum fluctuations may be introduced by additional exchange interactions involving spin flips (e.g. XY or more complex couplings), which naturally occur in some other pyrochlores like Yb 2 Ti 2 O 7 [8,9]. However, such quantum exchange models are quite complex, and their phase diagrams contain many other ground states in addition to the desired CQSL [10,11], so achieving the right type of quantum exchange requires some serendipity.At the model Hamiltonian level, a simpler route to "quantum-ize" classical spin ice is to add a transverse field. This is not achievable with a physical magnetic field, however, because the latter couples most strongly to the Ising spin components, i.e. it introduces longitudinal fields which quench fluctuations instead of enhancing them. However, it has been recently pointed out that for non-Kramer's rare earth ions like Ho 3+ or Pr 3+ , local electric field gradients play the role of transverse fields in the spin Hamiltonian while preserving time-reversal symmetry [2]. This provides a mechanism to induce transverse fields while protecting the system from longitudinal fields. In Ref. random transverse fields. Here, we consider a simpler possibility: straining a non-Kramers spin ice material to lower the local symmetry and thereby create a uniform transverse field. Large strains are achievable in thin f...

Quantum robustness of fracton phases

“…Padé and Dlog-Padé extrapolation schemes are standard methods in the field of series expansions as they allow for an evaluation of the series beyond their original radius of convergence [80]. Padé extrapolation is generally used for extrapolating ground-state energies [81], especially when critical fluctuations are absent as in the case of first-order phase transitions found for the perturbed fracton codes studied in this work. We therefore locate the phase-transition point and investigate the convergence of (multi-)fracton excitations energies via Padé extrapolations.…”

Symmetry enriched U(1) quantum spin liquids

“…[19][20][21]. In these models, the Z 2 × T symmetric U(1) quantum spin liquid states are (E b M b ) − .…”

“…Microscopic models for such phases were described in Refs. [15][16][17][18][19][20][21]. The emergence of the photon is necessarily accompanied by the emergence of quasiparticles carrying electric and/or magnetic charges that couple to the photon.…”

Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice

“…Quantum fluctuations and entanglement are introduced to such a classical Ising spin system upon adding transverse spin exchange interactions (leading to the XXZ model) 9 , or by applying a uniform magnetic field transverse to the quantization direction of the Ising spin exchange interactions 10 . It has been argued that, for non-Kramers degenerate rare-earth ions such as Dy 3+ and Ho 3+ , such effective transverse fields in the magnetic Hamiltonian derive from local electric field gradients 11,12 . While Ref.…”

“…12, the effective field strength h is controlled by the magnitude of the strain applied to the spin-ice material. Depending on the ratio h/J, the ground state of the Hamiltonian H furthermore exhibits two distinct phases 11,12 ; cf. the arXiv:1808.09827v2 [cond-mat.str-el] 3 Dec 2018 phase diagram in Fig.…”