Finite-temperature Transition Research Articles

Integrals of motion in the many-body localized phase

We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum {0,1}, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization–delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.

Collective modes and Kosterlitz-Thouless transition in a magnetic field in the planar Nambu–Jona-Lasinio model

It is known that a constant magnetic field is a strong catalyst of dynamical chiral symmetry breaking in 2+1 dimensions, leading to generating dynamical fermion mass even at weakest attraction. In this work we investigate the collective modes associated with the dynamical chiral symmetry breaking in a constant magnetic field in the (2+1)-dimensional Nambu--Jona-Lasinio model with continuous U(1) chiral symmetry. We introduce a self-consistent scheme to evaluate the propagators of the collective modes at the leading order in 1/N. The contributions from the vacuum and from the magnetic field are separated such that we can employ the well-established regularization scheme for the case of vanishing magnetic field. The same scheme can be applied to the study of the next-to-leading order correction in 1/N. We show that the sigma mode is always a lightly bound state with its mass being twice the dynamical fermion mass for arbitrary strength of the magnetic field. Since the dynamics of the collective modes is always 2+1 dimensional, the finite temperature transition should be of the Kosterlitz-Thouless (KT) type. We determine the KT transition temperature $T_{\rm KT}$ as well as the mass melting temperature $T^*$ as a function of the magnetic field. It is found that the pseudogap domain $T_{\rm KT}<T<T^*$ is enlarged with increasing strength of the magnetic field. The influence of a chiral imbalance or axial chemical potential $\mu_5$ is also studied. We find that even a constant axial chemical potential $\mu_5$ can lead to inverse magnetic catalysis of the KT transition temperature in 2+1 dimensions. The inverse magnetic catalysis behavior is actually the de Haas--van Alphen oscillation induced by the interplay between the magnetic field and the Fermi surface.

Interplay of topology and geometry in frustrated two-dimensional Heisenberg magnets

We investigate two-dimensional frustrated Heisenberg magnets using non-perturbative renormalization group techniques. These magnets allow for point-like topological defects which are believed to unbind and drive either a crossover or a phase transition which separates a low temperature, spin-wave dominated regime from a high temperature regime where defects are abundant. Our approach can account for the crossover qualitatively and both the temperature dependence of the correlation length as well as a broad but well defined peak in the specific heat are reproduced. We find no signatures of a finite temperature transition and an accompanying diverging length scale. Our analysis is consistent with a rapid crossover driven by topological defects.

Thermodynamics of lattice QCD with 3 flavors of color-sextet quarks. II. Nt=6 and Nt=8

We have been studying QCD with 2 flavours of colour-sextet quarks as a candidate walking-Technicolor theory using lattice-QCD simulations. The evolution of the coupling constant with lattice spacing is measured at the finite-temperature chiral transition to determine if this theory is asymptotically free and hence QCD-like. The lattice spacing is varied by changing the number of lattice sites, $N_t$, in the Euclidean time direction. QCD with 3 flavours is studied for comparison. Since this theory is expected to be conformal, with an infrared fixed point, the coupling constant at the chiral transition should approach a non-zero value as $N_t$ becomes large. Our earlier simulations on lattices with $N_t=4$ and $N_t=6$ exhibited a significant decrease in coupling at the chiral transition as $N_t$ was increased. We have now extended these simulations to $N_t=8$, and performed additional simulations at $N_t=6$ to measure the coupling constant at the chiral transition more precisely. These indicate that while there is an appreciable decrease in coupling between $N_t=6$ and $N_t=8$, this is much smaller than that between $N_t=4$ and $N_t=6$. Thus we are hopeful that we are approaching the large-$N_t$ limit. However, further simulations at larger $N_t$(s) are needed.

Quantum paraelectric glass state in SrCu3Ti4O12

Magnetic and dielectric studies of SrCu3Ti4O12 carried out over 5–300 K confirm antiferromagnetic (AFM) ordering of Cu-spins at TN = 23 K. Dielectric constant ε′ measured across 1 Hz-1 MHz signifies quantum paraelectric character, Barrett-fittable almost down to TN. Competition of athermal fluctuations and the literature-reported magneto-phonon-softening near TN manifest a quantum paraelectric glass (QPG) state. Emergent AFM-field tunes the otherwise quantum ordering (at absolute-zero) of the dipoles to finite-temperature kinetic glass transition; spectral dispersion of dielectric constant was unambiguously manifested and characterized. Vogel-Fulcher glass-kinetics parameterization sets the almost relaxation-free QPG state in SrCu3Ti4O12 apart from an emergent scaling-class, to which typical ferroelectric relaxors belong.

Publisher's Note: Nature of finite-temperature transition in anisotropic pyrochloreEr2Ti2O7[Phys. Rev. B89, 140403(R) (2014)

Publisher's Note: Nature of finite-temperature transition in anisotropic pyrochlore<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Er</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Ti</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>7</mml:mn></mml:msub></mml:math>[Phys. Rev. B<b>89</b>, 140403(R) (2014)

Shannon-Rényi entropies and participation spectra across three-dimensionalO(3)criticality

Universal features in the scalings of Shannon-R\'enyi entropies of many-body groundstates are studied for interacting spin-$\frac{1}{2}$ systems across (2+1) dimensional $O(3)$ critical points, using quantum Monte Carlo simulations on dimerized and plaquettized Heisenberg models on the square lattice. Considering both full systems and line shaped subsystems, $SU(2)$ symmetry breaking on the N\'eel ordered side of the transition is characterized by the presence of a logarithmic term in the scaling of Shannon-R\'enyi entropies, which is absent in the disordered gapped phase. Such a difference in the scalings allows to capture the quantum critical point using Shannon-R\'enyi entropies for line shaped subsystems of length $L$ embedded in $L\times L$ tori, as the smaller subsystem entropies are numerically accessible to much higher precision than for the full system. Most interestingly, at the quantum phase transition an additive subleading constant $b_\infty^{*\rm line}=0.41(1)$ emerges in the critical scaling of the line Shannon-R\'enyi entropy $S_\infty^\text{line}$. This number appears to be universal for 3d $O(3)$ criticality, as confirmed for the finite-temperature transition in the 3d antiferromagnetic spin-$\frac{1}{2}$ Heisenberg model. Additionally, the phases and phase transition can be detected in several features of the participation spectrum, consisting of the diagonal elements of the reduced density matrix of the line subsystem. In particular the N\'eel ordering transition can be simply understood in the $\{S^z\}$ basis by a confinement mechanism of ferromagnetic domain walls.

Nature of finite-temperature transition in anisotropic pyrochloreEr2Ti2O7

We study the finite-temperature transition in a model $XY$ antiferromagnet on a pyrochlore lattice, which describes the pyrochlore material ${\mathrm{Er}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. The ordered magnetic structure selected by thermal fluctuations is sixfold degenerate. Nevertheless, our classical Monte Carlo simulations show that the critical behavior corresponds to the three-dimensional $XY$ universality class. We determine an additional critical exponent ${\ensuremath{\nu}}_{6}=0.75&gt;\ensuremath{\nu}$ characteristic of a dangerously irrelevant scaling variable. Persistent thermal fluctuations in the ordered phase are revealed in Monte Carlo simulations by the peculiar coexistence of Bragg peaks and diffuse magnetic scattering, the feature also observed in neutron diffraction experiments.

QCD chiral transition,U(1)Asymmetry and the dirac spectrum using domain wall fermions

We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: $24^3\times8$ and $32^3\times8$, where the larger volume varies in linear size between 5.6 fm (at T=139 MeV) and 4.0 fm (at T=195 MeV). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, $16^3\times8$ volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the $\sua$ and $\ua$ symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudo-critical temperature, $T_c$, of approximately 165 MeV consistent with previous results and strong finite volume dependence below $T_c$. Clear evidence is seen for $\ua$ symmetry breaking above $T_c$ which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation.

Transition in coupled replicas may not imply a finite-temperature ideal glass transition in glass-forming systems.

A key open question in the glass transition field is whether a finite temperature thermodynamic transition to the glass state exists or not. Recent simulations of coupled replicas in atomistic models have found signatures of a static transition as a function of replica coupling. This can be viewed as evidence of an associated thermodynamic glass transition in the uncoupled system. We demonstrate here that a different interpretation is possible. We consider the triangular plaquette model, an interacting spin system which displays (East model-like) glassy dynamics in the absence of any static transition. We show that when two replicas are coupled, there is a curve of equilibrium phase transitions, between phases of small and large overlap, in the temperature-coupling plane (located on the self-dual line of an exact temperature-coupling duality of the system) which ends at a critical point. Crucially, in the limit of vanishing coupling the finite temperature transition disappears, and the uncoupled system is in the disordered phase at all temperatures. We discuss an interpretation of atomistic simulations in light of this result.

Relevance of the axial anomaly at the finite-temperature chiral transition in QCD

We investigate the nature of the finite-temperature chiral transition in QCD with two light flavors, in the case of an effective suppression of the the U(1)_A symmetry breaking induced by the axial anomaly, which implies the symmetry breaking U(2)_L X U(2)_R -> U(2)_V, instead of SU(2)_L X SU(2)_R -> SU(2)_V. For this purpose, we perform a high-order field-theoretical perturbative study of the renormalization-group (RG) flow of the corresponding three-dimensional multiparameter Landau-Ginzburg-Wilson Phi4 theory with the same symmetry-breaking pattern. We confirm the existence of a stable fixed point (FP), and determine its attraction domain in the space of the bare quartic parameters. Therefore, the chiral QCD transition might be continuous also if the U(1)_A symmetry is effectively restored at Tc. However, the corresponding universality class differs from the O(4) vector universality class which would describe a continuous transition in the presence of a substantial U(1)_A symmetry breaking at Tc. We estimate the critical exponents of the U(2)_L X U(2)_R -> U(2)_V universality class by computing and analyzing their high-order perturbative expansions. These results are important to discriminate among the different scenarios for the scaling behavior of QCD with two light flavors close to the chiral transition.

The low temperature magnetic phase diagram of EuxSr1−xTiO3

Specific heat and magnetization measurements demonstrate that the antiferromagnetic (AFM) phase transition at TN = 5.7 K of EuTiO3 is rapidly suppressed with Sr doping in EuxSr1−xTiO3. Close to x = 0.25, TN = 0 K and AFM order vanishes. Above this critical concentration a finite transition temperature to an AFM phase is observed. The exchange couplings are derived as a function of x and the corresponding low temperature phase diagram is presented.

Critical behavior of the ideal-gas Bose-Einstein condensation in the Apollonian network

We show that the ideal Boson gas displays a finite-temperature Bose-Einstein condensation transition in the complex Apollonian network exhibiting scale-free, small-world, and hierarchical properties. The single-particle tight-binding Hamiltonian with properly rescaled hopping amplitudes has a fractal-like energy spectrum. The energy spectrum is analytically demonstrated to be generated by a nonlinear mapping transformation. A finite-size scaling analysis over several orders of magnitudes of network sizes is shown to provide precise estimates for the exponents characterizing the condensed fraction, correlation size, and specific heat. The critical exponents, as well as the power-law behavior of the density of states at the bottom of the band, are similar to those of the ideal Boson gas in lattices with spectral dimension d(s)=2ln(3)/ln(9/5)~/=3.74.

Partial Order in Potts Models on the Generalized Decorated Square Lattice

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-nearest (J2) neighbor interactions. Using the tensor renormalization-group method augmented by higher order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution. For q = 3, we find a highly degenerate ground state with partial order on a single sublattice, but with vanishing entropy per site, and we obtain the phase diagram as a function of the ratio J2/J1. There is no finite-temperature transition for the q = 4 case when J1 = J2, whereas the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.

Topology across the finite temperature transition studied by overimproved cooling in gluodynamics and QCD

Gluodynamics and two-flavor QCD at non-zero temperature are studied with the so-called overimproved cooling technique under which caloron solutions may remain stable. We consider topological configurations either at the first occuring stable plateau of topological charge or at the first (anti)selfdual plateau and find the corresponding topological susceptibility at various temperatures on both sides of the thermal transition or crossover. In pure gluodynamics the topological susceptibility drops sharply at the deconfinement temperature while in full QCD it decreases smoothly at temperatures above the pseudocritical one. The results are close to those calculated by other methods. We interpret our findings in terms of the (in)stability of calorons with non-trivial holonomy and their dyon constituents against overimproved cooling.

Librational fluctuations in protein glasses

Librational motions in the region of the protein “glass” (or dynamic) transition are analysed for spin-labelled haemoglobin, serum albumin and β-lactoglobulin by EPR spectroscopy. A discontinuity in the temperature dependence of the mean-square librational amplitude, <α2>, occurs in the region of 200K as found for the mean-square atomic displacement, <r2>, at the protein dynamic transition by Mössbauer spectroscopy and neutron scattering. The discontinuity in <α2> vs. T can be described by the Vogel–Tammann–Fulcher equation, implying a finite glass transition temperature. Above the dynamic transition, <α2> vs. 1/T can be approximated by the Arrhenius law with activation energies similar to those usually found for <r2>, and relaxation processes in glass-forming media and the hydration shells of proteins. Similar results are found for librational fluctuations of membranous Na,K-ATPase spin-labelled either on superficial SH groups or on those essential to activity.

EFFECTS OF STRAIN COUPLING AND MARGINAL DIMENSIONALITY IN THE NATURE OF PHASE TRANSITION IN QUANTUM PARAELECTRICS

Here a recently observed weak first order transition in doped SrTiO 3 [Taniguchi, Itoh and Yagi, Phys. Rev. Lett.99, 017602 (2007)] is argued to be a consequence of the coupling between strain and order parameter fluctuations. Starting with a semi-microscopic action, and using renormalization group equations for vertices, we write the free energy of such a system. This fluctuation renormalized free energy is then used to discuss the possibility of first order transition at zero temperature as well as at finite temperature. An asymptotic analysis predicts small but a finite discontinuity in the order parameter near a mean field quantum critical point at zero temperature. In case of finite temperature transition, near quantum critical point such a possibility is found to be extremely weak. Results are in accord with some experimental findings on quantum paraelectrics such as SrTiO 3 and KTaO 3.

Critical parameters from trap-size scaling in systems of trapped particles

We investigate the critical behavior of trapped particle systems at the low-temperature superfluid transition. In particular, we consider the three-dimensional Bose-Hubbard model in the presence of a trapping harmonic potential coupled with the particle density, which is a realistic model of cold bosonic atoms in optical lattices. We present a numerical study based on quantum Monte Carlo simulations, analyzed in the framework of the trap-size scaling (TSS). We show how the critical parameters can be derived from the trap-size dependencies of appropriate observables, matching them with TSS. This provides a systematic scheme which is supposed to exactly converge to the critical parameters of the transition in the large-trap-size limit. Our numerical analysis may provide a guide for experimental investigations of trapped systems at finite-temperature and quantum transitions, showing how critical parameters may be determined by looking at the scaling of the critical modes with respect to the trap size, i.e., by matching the trap-size dependence of the experimental data with the expected TSS ansatz.

Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

Boolean decision problems with competing interactions on scale-free networks: Critical thermodynamics

We study the critical behavior of Boolean variables on scale-free networks with competing interactions (Ising spin glasses). Our analytical results for the disorder-network-decay-exponent phase diagram are verified using Monte Carlo simulations. When the probability of positive (ferromagnetic) and negative (antiferromagnetic) interactions is the same, the system undergoes a finite-temperature spin-glass transition if the exponent that describes the decay of the interaction degree in the scale-free graph is strictly larger than 3. However, when the exponent is equal to or less than 3, a spin-glass phase is stable for all temperatures. The robustness of both the ferromagnetic and spin-glass phases suggests that Boolean decision problems on scale-free networks are quite stable to local perturbations. Finally, we show that for a given decay exponent spin glasses on scale-free networks seem to obey universality. Furthermore, when the decay exponent of the interaction degree is larger than 4 in the spin-glass sector, the universality class is the same as for the mean-field Sherrington-Kirkpatrick Ising spin glass.