The magnetic analog of the Grüneisen parameter, i.e., the magnetocaloric effect, is a valuable tool for studying field-tuned quantum phase transitions. We determine the magnetic Grüneisen parameter of the one-dimensional random transverse-field Ising model, focusing on its lowtemperature behavior at the exotic infinite-randomness quantum critical point and in the associated quantum Griffiths phases. 1 Introduction Zero-temperature quantum phase transitions are characterized by a competition between different quantum ground states. The resulting quantum fluctuations often cause unconventional behavior of thermodynamic and transport properties in the vicinity of the
The magnetic analog of the Grüneisen parameter, i.e., the magnetocaloric effect, is a valuable tool for studying field-tuned quantum phase transitions. We determine the magnetic Grüneisen parameter of the one-dimensional random transverse-field Ising model, focusing on its lowtemperature behavior at the exotic infinite-randomness quantum critical point and in the associated quantum Griffiths phases. 1 Introduction Zero-temperature quantum phase transitions are characterized by a competition between different quantum ground states. The resulting quantum fluctuations often cause unconventional behavior of thermodynamic and transport properties in the vicinity of the
Abstract The magnetic analog of the Grüneisen parameter, that is, the magnetocaloric effect, is a valuable tool for studying field‐tuned quantum phase transitions. We determine the magnetic Grüneisen parameter of the one‐dimensional random transverse‐field Ising model, focusing on its low‐temperature behavior at the exotic infinite‐randomness quantum critical point and in the associated quantum Griffiths phases. We present extensive numerical simulations showing that the magnetic Grüneisen parameter diverges logarithmically with decreasing temperature in the quantum Griffiths phase. It changes sign right at criticality. These results confirm a recent strong‐disorder renormalization group theory. We also compare our findings to the behavior of the clean transverse‐field Ising chain.
We consider the behavior of the Gr\"uneisen parameter, the ratio between thermal expansion and specific heat, at pressure-tuned infinite-randomness quantum-critical points and in the associated quantum Griffiths phases. We find that the Gr\"uneisen parameter diverges as ln(T0/T) with vanishing temperature T in the quantum Griffiths phases. At the infinite-randomness critical point itself, the Gr\"uneisen parameter behaves as ${[\text{ln}({T}_{0}/T)]}^{1+1/(\ensuremath{\nu}\ensuremath{\psi})}$ where $\ensuremath{\nu}$ and $\ensuremath{\psi}$ are the correlation length and tunneling exponents. Analogous results hold for the magnetocaloric effect at magnetic-field-tuned transitions. We contrast clean and dirty systems, we discuss subtle differences between Ising and Heisenberg symmetries, and we relate our findings to recent experiments on ${\text{CePd}}_{1\ensuremath{-}x}{\text{Rh}}_{x}$.
The magnetic Grüneisen ratio, defined as Γ g ≡ (1/ T )(∂ T /∂ g ) S , characterizes the magnetocaloric effect (MCE) driven by an external field g and serves as a highly sensitive probe for field-induced quantum critical points (QCPs). Near a QCP, Γ g displays diverging behaviors described by a universal scaling function depending on the universality class. Here, we systematically investigate the universal scaling functions of Grüneisen ratio Γ g in typical one-dimensional (1D) and two-dimensional (2D) quantum spin systems, including the transverse-field Ising model, XY model, q -state quantum Potts model ( q = 3, 4), and the J 1 - J 2 columnar dimer model. Our approach employs the linearized tensor renormalization group (LTRG) method for infinite-size 1D systems and the stochastic series expansion quantum Monte Carlo (SSE QMC) simulations for 2D systems, enabling precise calculations of the Γ g near QCPs. We extract universal scaling functions via data collapse analysis. This universal magnetocaloric framework offers a quantitative tool for analyzing measurements in quantum materials and for guiding the search for quantum critical cooling applications.
We consider the scaling behavior of thermodynamic quantities in the one-dimensional transverse field Ising model near its quantum critical point (QCP). Our study has been motivated by the question about the thermodynamical signatures of this paradigmatic quantum critical system and, more generally, by the issue of how quantum criticality accumulates entropy. We find that the crossovers in the phase diagram of temperature and (the nonthermal control parameter) transverse field obey a general scaling ansatz, and so does the critical scaling behavior of the specific heat and magnetic expansion coefficient. Furthermore, the Gr\"uneisen ratio diverges in a power-law way when the QCP is accessed as a function of the transverse field at zero temperature, which follows the prediction of quantum critical scaling. However, at the critical field, upon decreasing the temperature, the Gr\"uneisen ratio approaches a constant instead of showing the expected divergence. We are able to understand this unusual result in terms of a peculiar form of the quantum critical scaling function for the free energy; the contribution to the Gr\"uneisen ratio vanishes at the linear order in a suitable Taylor expansion of the scaling function. In spite of this special form of the scaling function, we show that the entropy is still maximized near the QCP, as expected from the general scaling argument. Our results establish the telltale thermodynamic signature of a transverse-field Ising chain, and will thus facilitate the experimental identification of this model quantum-critical system in real materials.
We study quantum phase transitions in transverse-field Ising spin chains in which the couplings are random but hyperuniform, in the sense that their large-scale fluctuations are suppressed. We construct a one-parameter family of disorder models in which long-wavelength fluctuations are increasingly suppressed as a parameter $\ensuremath{\alpha}$ is tuned. For $\ensuremath{\alpha}=0$, one recovers the familiar infinite-randomness critical point. For $0<\ensuremath{\alpha}<1$, we find a line of infinite-randomness critical points with continuously varying critical exponents; however, the Griffiths phases that flank the critical point at $\ensuremath{\alpha}=0$ are absent at any $\ensuremath{\alpha}>0$. When $\ensuremath{\alpha}>1$, randomness is a dangerously irrelevant perturbation at the clean Ising critical point, leading to a state we call the critical Ising insulator. In this state, thermodynamics and equilibrium correlation functions behave as in the clean system. However, all finite-energy excitations are localized, thermal transport vanishes, and autocorrelation functions remain finite in the long-time limit. We characterize this line of hyperuniform critical points using a combination of perturbation theory, renormalization-group methods, and exact diagonalization.
We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.