Zero-temperature Entropy Research Articles

Higher-derivative corrections to black hole entropy at zero temperature

There is a well-established connection between the higher-derivative corrections to the black hole entropy and the black hole extremality bound. The particular combination of effective field theory (EFT) coefficients ${c}_{i}$ that controls the mass shift at fixed charge and temperature also controls the entropy shift at fixed charge and mass, in the limit where the mass approaches the uncorrected value for the extremal mass. In this paper, we use the classical entropy function formalism to examine the entropy corrections at exactly zero temperature, or at the corrected value for the extremal mass. We find that the zero-temperature entropy shift (a) is unrelated to the mass shift, (b) is $\mathcal{O}({c}_{i})$ in the EFT coefficients, rather than $\mathcal{O}(\sqrt{{c}_{i}})$, as is the constant-mass entropy shift, and (c) is negative in the example of the EFT arising at low energies from QED plus gravity.

Spin liquid to spin glass crossover in the random quantum Heisenberg magnet

We study quantum SU($M$) spins with all-to-all and random Heisenberg exchange interactions of root-mean-square strength $J$. The $M \rightarrow \infty$ model has a spin liquid ground state with the spinons obeying the equations of the Sachdev-Ye-Kitaev (SYK) model. Numerical studies of the SU(2) model with $S=1/2$ spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a $1/M$ expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order $q_{EA}$. The SYK spin liquid behavior persists down to a frequency $\omega_\ast \sim J q_{EA}$, and for $\omega < \omega_\ast$, the spectral density is linear in $\omega$, thus quenching the extensive zero temperature entropy of the spin liquid. The linear $\omega$ spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large $q_{EA}$. We argue that the extensive SYK spin liquid entropy is transformed as $T \rightarrow 0$ to an extensive complexity of the spin glass state.

Intrinsic disorder of dangling OH-bonds in the first water layer on noble metal surfaces

Using the first-principles calculation, we have systematically investigated the orientation of dangling OH-bonds in the first adsorbed water layer on close packed surface of noble metals (gold, platinum and palladium). We find that, the distribution of up and down dangling OH-bonds can strongly change the adsorption stability. A specific distribution of dangling OH-bonds is always indispensable in various adsorption patterns for its stability. The in-plane arrangement of water molecules also has important influence on the orientation of dangling OH-bonds. More importantly, the disorder in the orientation (up or down) of dangling OH manifests a kind of zero-temperature residual entropy in some absorption structures. In essence, the residual entropy arises from the competition between water-water and water-metal interactions, which is different from the counterpart in ice crystals.

The Number of Optimal Matchings for Euclidean Assignment on the Line

We consider the Random Euclidean Assignment Problem in dimension d=1, with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings (say, sim exp (S_N) at size N). We characterize all possible optimal matchings of a given instance of the problem, and we give a simple product formula for their number. Then, we study the probability distribution of S_N (the zero-temperature entropy of the model), in the uniform random ensemble. We find that, for large N, S_N sim frac{1}{2} N log N + N s + {mathcal {O}}left( log N right) , where s is a random variable whose distribution p(s) does not depend on N. We give expressions for the moments of p(s), both from a formulation as a Brownian process, and via singularity analysis of the generating functions associated to S_N. The latter approach provides a combinatorial framework that allows to compute an asymptotic expansion to arbitrary order in 1/N for the mean and the variance of S_N.

Magnetocaloric Effect in Two-Dimensional Diluted Ising Model: Appearance of Frustrations in the Ground State

The magnetocaloric effect in a two-dimensional Ising model is considered for different ratios between parameters of inter-site repulsion of nonmagnetic impurities and exchange coupling. Classical Monte Carlo simulations on a square lattice show that in case of weak coupling and at sufficiently high concentrations of nonmagnetic impurities the long-range ferromagnetic ordering breaks down to give isolated spin clusters in the ground state of the system. This leads to appearance of a paramagnetic response in the system at the zero temperature and nonzero entropy of the ground state. The feasibility to detect frustration of ground state using data on the magnetic entropy variation is discussed

Generalized Ising Model in the Absence of Magnetic Field

The Ising model on an one-dimensional monoatomic equidistant lattice with different exchange interactions between atomic spins at the sites of nearest neighbors and different interactions between atomic spins at the sites of second neighbors is investigated. The generalized Kramers–Wannier transfer matrix with translation on two periods of a lattice is derived. The phase diagrams representing all possible magnetic types of ordering in the ground state are constructed. Many triple points of intersection of phases and lines of pair coexistence of phases in strict accordance with the Gibbs phase rule are found and a property similar to supercooling and superheating is detected. It is shown that at triple points the phases are not individualized but significantly frustrated, which corresponds to the phenomenon of critical opalescence. Exact analytical expressions for the Gibbs free energy, as well as for such thermodynamic characteristics of the system as internal energy, heat capacity and entropy including zero-temperature entropy are derived. A variety of particular cases are analyzed and a comparison is made with all known results including on a two-dimensional lattice.

Notes on the complex Sachdev-Ye-Kitaev model

We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with N ≫ 1 flavors and a global U(1) charge. We provide a general definition of the charge in the (G, Σ) formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.

Reentrance of the topological phase in a spin-1 frustrated Heisenberg chain

For the Haldane phase, the magnetic field usually tends to break the symmetry and drives the system into a topologically trivial phase. Here, we report a novel reentrance of the Haldane phase at zero temperature in the spin-1 antiferromagnetic Heisenberg model on sawtooth chain. A partial Haldane phase is induced by the magnetic field, which is the combination of the Haldane state in one sublattice and a ferromagnetically ordered state in the other sublattice. Such a partial topological order is a result of the zero-temperature entropy due to quantum fluctuations caused by geometrical frustration.

Classical glasses, black holes, and strange quantum liquids

From the dynamics of a broad class of classical mean-field glass models one may obtain a quantum model with finite zero-temperature entropy, a quantum transition at zero temperature, and a time-reparametrization (quasi-)invariance in the dynamical equations for correlations. The low eigenvalue spectrum of the resulting quantum model is directly related to the structure and exploration of metastable states in the landscape of the original classical glass model. This mapping reveals deep connections between classical glasses and the properties of SYK-like models.

Ordering and frustrations in generalized Ising chain

The Ising model on a one-dimensional monoatomic equidistant lattice with different nearest-neighbour and second-neighbour exchange interactions is researched. Generalized Kramers-Wannier transfer-matrix with translation on two periods of a lattice is introduced. A property similar to supercooling and superheating is detected. At the triple points phases are not individualized, but completely frustrated which corresponds to the phenomenon of critical opalescence. Exact analytical expressions for free energy, heat capacity and entropy including zero-temperature entropy are obtained. Various new special cases were analyzed and compared with all known results. All frustration fields for magnetization, frustration values for the zero-temperature entropy and magnetization are found.

Magnetic and magnetocaloric properties of the exactly solvable mixed-spin Ising model on a decorated triangular lattice in a magnetic field

The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing points, while the latter one occurs in some paramagnetic phases due to a spin frustration to be present at zero magnetic field. The inverse magnetocaloric effect can also be detected slightly above continuous phase transitions following the power-law dependence |−ΔSisomin|∝hn, where n depends basically on the ground-state spin ordering.

Qualitative breakdown of the noncrossing approximation for the symmetric one-channel Anderson impurity model at all temperatures

The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its non-crossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-$1/2$ particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any temperature, even when the approximation gives the exact threshold exponents of the ionic states. Actually, the NCA solution describes an overscreened Kondo effect, because it is the same as for the two-channel infinite-$U$ single level Anderson model. We explicitly show that the NCA is unable to distinguish between these two very different physical systems, independently of temperature. Using the impurity entropy as an example, we show that the low temperature values of the NCA entropy for the symmetric case yield the limit $S_{imp}(T=0)\rightarrow \ln\sqrt{2},$ which corresponds to the zero temperature entropy of the overscreened Kondo model. Similar pathologies are predicted for any other thermodynamic property. On the other hand, we have found that the OCA approach lifts the artificial mapping between the models and restores correct properties of the ground-state, for instance, a vanishing entropy at low enough temperatures $S_{imp}(T=0)\rightarrow0$. Our results indicate that the very well known NCA should be used with caution close to the symmetric point of the Anderson model.

Impurity entropy of junctions of multiple quantum wires

We calculate the zero-temperature impurity entropy of a junction of multiple quantum wires of interacting spinless fermions. Starting from a given single-particle S-matrix representing a fixed point of the renormalization group (RG) flows, we carry out fermionic perturbation theory in the bulk interactions, with the perturbation series summed in the random phase approximation (RPA). The results agree completely with boundary conformal field theory (BCFT) predictions of the ground state degeneracy, and also with known RG flows through the g -theorem.

Suppression of Pauling's residual entropy in the dilute spin ice(Dy1−xYx)2Ti2O7

Around 0.5 K, the entropy of the spin-ice Dy$_2$Ti$_2$O$_7$ has a plateau-like feature close to Pauling's residual entropy derived originally for water ice, but an unambiguous quantification towards lower temperature is prevented by ultra-slow thermal equilibration. Based on specific heat data of (Dy$_{1-x}$Y$_x$)$_2$Ti$_2$O$_7$ we analyze the influence of non-magnetic dilution on the low-temperature entropy. With increasing x, the ultra-slow thermal equilibration rapidly vanishes, the low-temperature entropy systematically decreases and its temperature dependence strongly increases. These data suggest that a non-degenerate ground state is realized in (Dy$_{1-x}$Y$_x$)$_2$Ti$_2$O$_7$ for intermediate dilution. This contradicts the expected zero-temperature residual entropy obtained from a generalization of Pauling's theory for dilute spin ice, but is supported by Monte Carlo simulations.

Intermediate scalings in holographic RG flows and conductivities

We construct numerically finite density domain-wall solutions which interpolate between two $AdS_4$ fixed points and exhibit an intermediate regime of hyperscaling violation, with or without Lifshitz scaling. Such RG flows can be realized in gravitational models containing a dilatonic scalar and a massive vector field with appropriate choices of the scalar potential and couplings. The infrared $AdS_4$ fixed point describes a new ground state for strongly coupled quantum systems realizing such scalings, thus avoiding the well-known extensive zero temperature entropy associated with $AdS_2 \times \mathbb{R}^2$. We also examine the zero temperature behavior of the optical conductivity in these backgrounds and identify two scaling regimes before the UV CFT scaling is reached. The scaling of the conductivity is controlled by the emergent IR conformal symmetry at very low frequencies, and by the intermediate scaling regime at higher frequencies.

Quantum phase transitions and thermodynamics of the power-law Kondo model

We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho(\omega) \sim |\omega|^r$, with exponent $-1<r<0$. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents $r$ and $(-r)$, combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.

Fermi surfaces inN=4super-Yang-Mills theory

We investigate and classify Fermi surface behavior for a set of fermionic modes in a family of backgrounds holographically dual to $\mathcal{N}=4$ super-Yang-Mills theory at zero temperature with two distinct chemical potentials. We numerically solve fluctuation equations for every spin-$1/2$ field in five-dimensional maximally supersymmetric gauged supergravity not mixing with gravitini. Different modes manifest two, one, or zero Fermi surface singularities, all associated with non-Fermi liquids, and we calculate dispersion relations and widths of excitations. We study two limits where the zero-temperature entropy vanishes. In one limit, a Fermi surface approaches a marginal Fermi liquid, which we demonstrate analytically, and conductivity calculations show a hard gap with the current dual to the active gauge field superconducting, while the other is insulating. In the other limit, conductivities reveal a soft gap with the roles of the gauge fields reversed.

Majorana fermions in superconducting helical magnets

In a variety of rare-earth based compounds singlet superconductivity coexists with helical magnetism. Here we demonstrate that surfaces of these systems should generically host a finite density of zero-energy Majorana modes. In the limit of vanishing disorder, these modes lead to a divergent contribution to zero-energy density of states and to zero-temperature entropy proportional to the sample surface area. When confined to a wire geometry, a discrete number of Majorana modes can be isolated. The relatively large characteristic energy scales for superconductivity and magnetism, compared to other proposals, as well as the lack of need for fine-tuning, make helical magnetic superconducting compounds favorable for the observation and experimental investigation of Majorana fermions.

ENTROPY IN QUANTUM CHROMODYNAMICS

We review the role of zero-temperature entropy in several closely-related contexts in QCD. The first is entropy associated with disordered condensates, including [Formula: see text]. The second is effective vacuum entropy arising from QCD solitons such as center vortices, yielding confinement and chiral symmetry breaking. The third is entanglement entropy, which is entropy associated with a pure state, such as the QCD vacuum, when the state is partially unobserved and unknown. Typically, entanglement entropy of an unobserved three-volume scales not with the volume but with the area of its bounding surface. The fourth manifestation of entropy in QCD is the configurational entropy of light-particle world-lines and flux tubes; we argue that this entropy is critical for understanding how confinement produces chiral symmetry breakdown, as manifested by a dynamically-massive quark, a massless pion, and a [Formula: see text] condensate.

Frustrated Ising Model on a Diamond Hierarchical Lattice

A frustrated Ising model on a diamond hierarchical lattice is studied. We obtain the exact partition function of this model and calculate the transition temperature, specific heat, entropy, magnetization, and ferromagnetic correlation function. Depending on the magnitude of a parameter giving the frustration, there exist three types of ground states: ferromagnetic, classical spin-liquid with highly developed short-range order, and paramagnetic. The dependence of the zero-temperature entropy on the frustration parameter has an infinite number of steps. The temperature dependence of the specific heat exhibits many peaks with decreasing temperature and entropy loss. The dominant spin configurations at low temperatures are also specified.