Quantum fluctuations can promote or inhibit glass formation

Abstract

Glasses are dynamically arrested states of matter that do not exhibit the long-range periodic structure of crystals 1-4 . Here we develop new insights from theory and simulation into the impact of quantum fluctuations on glass formation. As intuition may suggest, we observe that large quantum fluctuations serve to inhibit glass formation as tunnelling and zero-point energy allow particles to traverse barriers facilitating movement. However, as the classical limit is approached a regime is observed in which quantum effects slow down relaxation making the quantum system more glassy than the classical system. This dynamical 'reentrance' occurs in the absence of obvious structural changes and has no counterpart in the phenomenology of classical glass-forming systems.Although a wide variety of glassy systems ranging from metallic to colloidal can be accurately described using classical theory, quantum systems ranging from molecular, to electronic and magnetic form glassy states 5,6 . Perhaps the most intriguing of these is the coexistence of superfluidity and dynamical arrest, namely the 'superglass' state suggested by recent numerical, theoretical and experimental work [7][8][9] . Although such intriguing examples exist, at present there is no unifying framework to treat the interplay between quantum and glassy fluctuations in the liquid state.To attempt to formulate a theory for a quantum liquid to glass transition, we may first appeal to the classical case for guidance. Here, a microscopic theory exists in the form of mode-coupling theory (MCT), which requires only simple static structural information as input and produces a full range of dynamical predictions for time correlation functions associated with single-particle and collective fluctuations 10 . Although MCT has a propensity to overestimate a liquid's tendency to form a glass, it has been shown to account for the emergence of the non-trivial growing dynamical length scales associated with vitrification 11 . Perhaps more importantly, MCT has made numerous non-trivial predictions ranging from logarithmic temporal decay of density fluctuations and reentrant dynamics in adhesive colloidal systems to various predictions concerning the effect of compositional mixing on glassy behaviour 12,13 . These have been confirmed by both simulation and experiment [14][15][16] .A fully microscopic quantum version of MCT (QMCT) that requires only the observable static structure factor as input may be developed along the same lines as the classical version. Indeed, a zero-temperature version of such a theory has been developed and successfully describes the wave-vector-dependent dispersion in superfluid helium 17 . In the Supplementary Information, we outline the derivation of a full temperature-dependent QMCT. In the limit of high temperatures, our theory reduces to the hard-sphere fluid. φ is the volume fraction, Λ * = (βh 2 /mσ 2 ) 1/2 is the thermal wavelength in units of inter-particle separation σ , and β = 1/k B T is the inverse temperature. The approach by which the...

Anomalously large isotope effect in the glass transition of water

“…The relevance of quantum effects at a temperature T is usually quantified by the ratio of the thermal wavelength, Z= ffiffiffiffiffiffiffiffiffiffiffiffi ffi k B MT p , to the particle size a, Λ* = Z= ffiffiffiffiffiffiffiffiffiffiffiffi ffi k B MT p =a. When Λ* is ∼0.1 or larger, quantum effects cannot be neglected (7,26). Estimates at T ∼136 K give Λ* = 0.06 for H 2 O and 0.05 for D 2 O, indeed close to 0.1.…”

Facilitated Spin Models of Dissipative Quantum Glasses

“…From this perspective, slowdown, heterogeneity and other fluctuation features of glasses are rooted in the complex structure of trajectory space. This theory has emerged from the study of a class of idealized lattice systems, so-called kinetically constrained models, of which the simplest representatives are the facilitated spin models [7].Quantum glasses, just like their classical counterparts, are of much current interest, among other reasons due to their relevance to issues like supersolidity [8], quantum annealing [9], glassiness in electronic systems [10], thermalization and many-body localization [11], and arrest in quantum fluids [12]. Central questions in quantum many-body systems which display glassy behaviour…”

“…Quantum glasses, just like their classical counterparts, are of much current interest, among other reasons due to their relevance to issues like supersolidity [8], quantum annealing [9], glassiness in electronic systems [10], thermalization and many-body localization [11], and arrest in quantum fluids [12]. Central questions in quantum many-body systems which display glassy behaviour…”

Observation of crystallization slowdown in supercooled parahydrogen and orthodeuterium quantum liquid mixtures

“…However, diverse drawbacks such as polydispersity and sedimentation often make the experimental data from these systems difficult to interpret [8,9]. Accessing the details of the crystallization process in simple atomic and molecular counterparts, on the other hand, remains an experimental challenge due to relevant time scales that are orders of magnitude shorter.Theoretical studies have shown that the inclusion of quantum effects adds a further degree of complexity in the behavior of supercooled liquids, leading to novel exotic phenomena such as superfluidity [10,11] or enhanced dynamical slowing down [12][13][14]. Yet again, the difficulties in supercooling a quantum liquid to very low temperatures have so far precluded possible experimental studies of the interplay of quantum effects and structural transformations in nonequilibrium bulk liquids.…”

“…Theoretical studies have shown that the inclusion of quantum effects adds a further degree of complexity in the behavior of supercooled liquids, leading to novel exotic phenomena such as superfluidity [10,11] or enhanced dynamical slowing down [12][13][14]. Yet again, the difficulties in supercooling a quantum liquid to very low temperatures have so far precluded possible experimental studies of the interplay of quantum effects and structural transformations in nonequilibrium bulk liquids.…”