100 Glorious Years of the Ising Model
This is an editorial article based on the reseaches on the Ising model over the last 100 years.
cond-mat.stat-mech↗
arXiv subjects
Ferenc Igloi
Publications and source records attributed to Ferenc Igloi.
Quench dynamics of the quantum XXZ chain with staggered interactions: Exact results and simulations on digital quantum computers
We investigate quench dynamics in the quantum $S=1/2$ XXZ antiferromagnetic chain with staggered and anisotropic interactions in the flat-band limit. We consider global quenches that interchange odd- and even-bond strengths in a fully dimerized chain, yielding a postquench Hamiltonian with couplings only on even links. Due to the vanishing group velocity of excitations, the system fails to relax, providing an ideal setting to study dynamical topological quantum phase transitions. We show that the $z$-component of the interactions, controlled by the anisotropy $\Delta$, acts as a relevant term that generates additional dynamical quantum phase transitions and induces rich structures in the Loschmidt echo. These transitions are symmetry-protected and robust for quenches between distinct dimerization patterns. Using a Bell-basis representation, we derive closed-form results for entanglement entropies, Loschmidt echoes for finite and infinite systems, and identify both $\Delta$-independent and $\Delta$-dependent critical times. Quantum simulations on IBM Quantum processors demonstrate that key observables can be reliably extracted on noisy intermediate-scale devices without error mitigation.
quant-ph↗
Correlated clusters of closed reaction centers during induction of intact cells of photosynthetic bacteria
Antenna systems serve to absorb light and to transmit excitation energy to the reaction center (RC) in photosynthetic organisms. As the emitted (bacterio)chlorophyll fluorescence competes with the photochemical utilization of the excitation, the measured fluorescence yield is informed by the migration of the excitation in the antenna. In this work, the fluorescence yield concomitant with the oxidized dimer (P+) of the RC were measured during light excitation (induction) and relaxation (in the dark) for whole cells of photosynthetic bacterium Rhodobacter sphaeroides lacking cytochrome c_2 as natural electron donor to P+ (mutant cycA). The relationship between the fluorescence yield and P+ (fraction of closed RC) showed deviations from the standard Joliot-Lavergne-Trissl model: 1) the hyperbola is not symmetric and 2) exhibits hysteresis. These phenomena originate from the difference between the delays of fluorescence relative to P+ kinetics during induction and relaxation, and in structural terms from the non-random distribution of the closed RCs during induction. The experimental findings are supported by Monte Carlo simulations and by results from statistical physics based on random walk approximations of the excitation in the antenna. The applied mathematical treatment demonstrates the generalization of the standard theory and sets the stage for a more adequate description of the long-debated kinetics of fluorescence and of the delicate control and balance between efficient light harvest and photoprotection in photosynthetic organisms.
physics.bio-ph↗
Critical quench dynamics of random quantum spin chains: Ultra-slow relaxation from initial order and delayed ordering from initial disorder
By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the average magnetization, $\overline{m}(t)$, of the random transverse-field Ising chain after global quenches. We observe different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by $\overline{m}(t) \sim \ln^a t$, and in a finite sample of length $L$ the average magnetization saturates at a size-dependent plateau $\overline{m}_p(L) \sim L^{-b}$; here the two exponents satisfy the relation $b/a=ψ=1/2$. Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until $t=t_d$ with $\ln t_d \sim L^ψ$ and then starts to increase until it saturates to an asymptotic value $\overline{m}_p(L) \sim L^{-b'}$, with $b'\approx 1.5$. For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable $\ln t/L^ψ$. Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.
cond-mat.dis-nn↗
Corner contribution to percolation cluster numbers in three dimensions
In three-dimensional critical percolation we study numerically the number of clusters, $N_Γ$, which intersect a given subset of bonds, $Γ$. If $Γ$ represents the interface between a subsystem and the environment, then $N_Γ$ is related to the entanglement entropy of the critical diluted quantum Ising model. Due to corners in $Γ$ there are singular corrections to $N_Γ$, which scale as $b_Γ \ln L_Γ$, $L_Γ$ being the linear size of $Γ$ and the prefactor, $b_Γ$, is found to be universal. This result indicates that logarithmic finite-size corrections exist in the free-energy of three-dimensional critical systems.
cond-mat.stat-mech↗
Nonequilibrium quench dynamics in quantum quasicrystals
We study the nonequilibrium dynamics of a quasiperiodic quantum Ising chain after a sudden change in the strength of the transverse field at zero temperature. In particular we consider the dynamics of the entanglement entropy and the relaxation of the magnetization. The entanglement entropy increases with time as a power-law, and the magnetization is found to exhibit stretched-exponential relaxation. These behaviors are explained in terms of anomalously diffusing quasiparticles, which are studied in a wave packet approach. The nonequilibrium magnetization is shown to have a dynamical phase transition.
cond-mat.stat-mech↗
Entanglement entropy dynamics of disordered quantum spin chains
By means of free fermionic techniques we study the time evolution of the entanglement entropy, S(t), of a block of spins in the random transverse-field Ising chain after a sudden change of the parameters of the Hamiltonian. We consider global quenches, when the parameters are modified uniformly in space, as well as local quenches, when two disconnected blocks are suddenly joined together. For a non-critical final state, the dynamical entanglement entropy is found to approach a finite limiting value for both types of quenches. If the quench is performed to the critical state, the entropy grows for an infinite block as S(t) \sim ln ln t. This type of ultraslow increase is explained through the strong disorder renormalization group method.
cond-mat.stat-mech↗
Infinite disorder scaling of random quantum magnets in three and higher dimensions
Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well as for Erd\H os-Rényi random graphs, which represent infinite dimensional lattices. In all studied cases an infinite disorder quantum critical point is identified, which ensures that the applied method is asymptotically correct and the calculated critical exponents tend to the exact values for large scales. We have found that the critical exponents are independent of the form of (ferromagnetic) disorder and they vary smoothly with the dimensionality.
cond-mat.dis-nn↗
Numerical study of the critical behavior of the Ashkin-Teller model at a line defect
We consider the Ashkin-Teller model on the square lattice, which is represented by two Ising models ($σ$ and $τ$) having a four-spin coupling of strength, $ε$, between them. We introduce an asymmetric defect line in the system along which the couplings in the $σ$ Ising model are modified. In the Hamiltonian version of the model we study the scaling behavior of the critical magnetization at the defect, both for $σ$ and for $τ$ spins by density matrix renormalization. For $ε>0$ we observe identical scaling for $σ$ and $τ$ spins, whereas for $ε<0$ one model becomes locally ordered and the other locally disordered. This is different of the critical behavior of the uncoupled model ($ε=0$) and is in contradiction with the results of recent field-theoretical calculations.
cond-mat.stat-mech↗
Nonequilibrium phase transition in a driven Potts model with friction
We consider magnetic friction between two systems of $q$-state Potts spins which are moving along their boundaries with a relative constant velocity $v$. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state which is far from equilibrium. The problem is treated analytically in the limit $v=\infty$ (in one dimension, as well as in two dimensions for large-$q$ values) and for $v$ and $q$ finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.
cond-mat.stat-mech↗
Renormalization group study of the two-dimensional random transverse-field Ising model
The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we study the model on the square lattice with a very efficient numerical implementation of the strong disorder renormalization group method, which makes us possible to treat finite samples of linear size up to $L=2048$. We have calculated sample dependent pseudo-critical points and studied their distribution, which is found to be characterized by the same shift and width exponent: $ν=1.24(2)$. For different types of disorder the infinite disorder fixed point is shown to be characterized by the same set of critical exponents, for which we have obtained improved estimates: $x=0.982(15)$ and $ψ=0.48(2)$. We have also studied the scaling behavior of the magnetization in the vicinity of the critical point as well as dynamical scaling in the ordered and disordered Griffiths phases.
cond-mat.dis-nn↗
On reduced density matrices for disjoint subsystems
We show that spin and fermion representations for solvable quantum chains lead in general to different reduced density matrices if the subsystem is not singly connected. We study the effect for two sites in XX and XY chains as well as for sublattices in XX and transverse Ising chains.
cond-mat.stat-mech↗
Disordered Potts model on the diamond hierarchical lattice: Numerically exact treatment in the large-q limit
We consider the critical behavior of the random q-state Potts model in the large-q limit with different types of disorder leading to either the nonfrustrated random ferromagnet regime or the frustrated spin glass regime. The model is studied on the diamond hierarchical lattice for which the Migdal-Kadanoff real-space renormalization is exact. It is shown to have a ferromagnetic and a paramagnetic phase and the phase transition is controlled by four different fixed points. The state of the system is characterized by the distribution of the interface free energy P(I) which is shown to satisfy different integral equations at the fixed points. By numerical integration we have obtained the corresponding stable laws of nonlinear combination of random numbers and obtained numerically exact values for the critical exponents.
cond-mat.dis-nn↗
Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions
We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, $w \le 20$, by numerical application of the strong disorder renormalization group method. We demonstrate that the critical properties of the ladders for any finite $w$ are controlled by the infinite disorder fixed point of the random chain and the correction to scaling exponents contain information about the two-dimensional model. We calculate sample dependent pseudo-critical points and study the shift of the mean values as well as scaling of the width of the distributions and show that both are characterized by the same exponent, $ν(2d)$. We also study scaling of the critical magnetization, investigate critical dynamical scaling as well as the behavior of the critical entanglement entropy. Analyzing the $w$-dependence of the results we have obtained accurate estimates for the critical exponents of the two-dimensional model: $ν(2d)=1.25(3)$, $x(2d)=0.996(10)$ and $ψ(2d)=0.51(2)$.
cond-mat.dis-nn↗
Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
Using free-fermionic techniques we study the entanglement entropy of a block of contiguous spins in a large finite quantum Ising chain in a transverse field, with couplings of different types: homogeneous, periodically modulated and random. We carry out a systematic study of finite-size effects at the quantum critical point, and evaluate subleading corrections both for open and for periodic boundary conditions. For a block corresponding to a half of a finite chain, the position of the maximum of the entropy as a function of the control parameter (e.g. the transverse field) can define the effective critical point in the finite sample. On the basis of homogeneous chains, we demonstrate that the scaling behavior of the entropy near the quantum phase transition is in agreement with the universality hypothesis, and calculate the shift of the effective critical point, which has different scaling behaviors for open and for periodic boundary conditions.
cond-mat.stat-mech↗
Scaling properties at the interface between different critical subsystems: The Ashkin-Teller model
We consider two critical semi-infinite subsystems with different critical exponents and couple them through their surfaces. The critical behavior at the interface, influenced by the critical fluctuations of the two subsystems, can be quite rich. In order to examine the various possibilities, we study a system composed of two coupled Ashkin-Teller models with different four-spin couplings epsilon, on the two sides of the junction. By varying epsilon, some bulk and surface critical exponents of the two subsystems are continuously modified, which in turn changes the interface critical behavior. In particular we study the marginal situation, for which magnetic critical exponents at the interface vary continuously with the strength of the interaction parameter. The behavior expected from scaling arguments is checked by DMRG calculations.
cond-mat.stat-mech↗
Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state
The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.
cond-mat.stat-mech↗
Entanglement entropy at infinite randomness fixed points in higher dimensions
The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite randomness fixed point in the diluted transverse Ising model in higher dimensions.
cond-mat.dis-nn↗