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Joachim Stolze

Publications and source records attributed to Joachim Stolze.

32 records · Page 2Linked to original sources
arXiv2008

Dynamic properties of quantum spin chains: Simple route to complex behavior

We examine dynamic structure factors of spin-1/2 chains with nearest-neighbor interactions of XX and Dzyaloshinskii-Moriya type, and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.

cond-mat.str-el↗
arXiv2007

Exact dynamics in the inhomogeneous central-spin model

We study the dynamics of a single spin-1/2 coupled to a bath of spins-1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. This formula is evaluated explicitly for initial conditions such that the bath spins are completely polarized at the beginning. For this case we find, after an initial decay, a persistent oscillatory behaviour of the central spin. For a large number of bath spins $N_b$, the oscillation frequency is proportional to $N_b$, whereas the amplitude behaves like $1/N_b$, to leading order. No asymptotic decay due to the non-uniform couplings is observed, in contrast to some recent studies.

cond-mat.stat-mech↗
arXiv2007

Spin- and entanglement-dynamics in the central spin model with homogeneous couplings

We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviors is found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the central spin decays to zero in the thermodynamic limit, while its entanglement entropy becomes maximal. On the other hand, if the unpolarized environment is initially in an eigenstate of the total bath spin, the central spin and the entanglement entropy exhibit persistent monochromatic large-amplitude oscillations. This raises the question to what extent entanglement of the bath spins prevents decoherence of the central spin.

cond-mat.stat-mech↗
arXiv2006

The Mott-Hubbard Transition on the D=infinity Bethe Lattice

In view of a recent controversy we investigated the Mott-Hubbard transition in D=infinity with a novel cluster approach. i) We show that any truncated Bethe lattice of order n can be mapped exactly to a finite Hubbard-like cluster. ii) We evaluate the self-energy numerically for n=0,1,2 and compare with a series of self-consistent equation-of-motion solutions. iii) We find the gap to open continously at the critical U_c~2.5t* (t = t* / sqrt{4d}). iv) A low-energy theory for the Mott-Hubbard transition is developed and relations between critical exponents are presented.

cond-mat.str-el↗
arXiv2005

Multiparticle entanglement and ranks of density matrices

Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we obtain necessary conditions for the separability of a given mixed state with respect to partitions of all particles of the system into subsets. The special case of pure states is discussed separately.

quant-ph↗
arXiv2005

Spin Chains as Perfect Quantum State Mirrors

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.

quant-ph↗
arXiv2005

Dimer and trimer fluctuations in the s=1/2 transverse XX chain

Exact results for the dynamic dimer and trimer structure factors of the one-dimensional s=1/2 XX model in a transverse magnetic field ($\parallel z$) are presented and discussed in relation to known exact results for the dynamic spin structure factors. In the framework of the Jordan-Wigner representation, the accessible spectrum of the dimer fluctuation operator is limited to two-fermion excitations whereas that of the trimer fluctuation operator involves two-fermion and four-fermion excitations. The spectral boundaries, soft modes, and singularity structure of the four-fermion excitation continuum as probed by the dynamic trimer structure factor are examined and compared with corresponding properties of the two-fermion excitation continuum, as probed by the dynamic dimer and transverse spin structure factors.

cond-mat.stat-mech↗
arXiv1999

Impurity spin relaxation in S=1/2 XX chains

Dynamic autocorrelations $ $ (α=x,z) of an isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin, defined by a local change in the nearest-neighbor coupling, is either in the bulk or at the boundary of the open-ended chain. The exact numerical calculation of the correlations employs the Jordan-Wigner mapping from spin operators to Fermi operators; effects of finite system size can be eliminated. Two distinct temperature regimes are observed in the long-time asymptotic behavior. At T=0 only power laws are present. At high T the x correlation decays exponentially (except at short times) while the z correlation still shows an asymptotic power law (different from the one at T=0) after an intermediate exponential phase. The boundary impurity correlations follow power laws at all T. The power laws for the z correlation and the boundary correlations can be deduced from the impurity-induced changes in the properties of the Jordan-Wigner fermion states.

cond-mat.stat-mech↗
arXiv1996

Dynamic correlations of antiferromagnetic spin-1/2 XXZ chains at arbitrary temperature from complete diagonalization

All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J \sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + ΔS_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $Δ=0 , \cos(0.3π)$, and 1. The dynamic spin pair correlations $< S_{l+n}^μ(t) S_l^μ > , (μ=x,z)$, the dynamic structure factors $S^μ(q,ω)$, and the intermediate structure factors $I^μ(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,ω)$ is mainly concentrated on the region $|ω| < \varepsilon_2(q)$, where $\varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^μ(q,t)$ for $Δ\neq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.

cond-mat.stat-mech↗
arXiv1996

Charge and spin dynamics in the one-dimensional $t-J_z$ and $t-J$ models

The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttinger-liquid ground state of the 1D $t-J$ model is assessed by comparison with the same quantities in the 1D $t-J_z$ model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At $J_z/t=0^+$ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. The $t-J_z$ charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the $t-J$ model. In the $t-J_z$ model, phase separation is accompanied by Néel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the $t-J$ model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by 2-spinon excitations) in the phase-separated state.

cond-mat↗
arXiv1995

Spin correlation functions in random-exchange s=1/2 XXZ chains

The decay of (disorder-averaged) static spin correlation functions at T=0 for the one-dimensional spin-1/2 XXZ antiferromagnet with uniform longitudinal coupling $JΔ$ and random transverse coupling $Jλ_i$ is investigated by numerical calculations for ensembles of finite chains. At $Δ=0$ (XX model) the calculation is based on the Jordan-Wigner mapping to free lattice fermions for chains with up to N=100 sites. At $Δ\neq 0$ Lanczos diagonalizations are carried out for chains with up to N=22 sites. The longitudinal correlation function $ $ is found to exhibit a power-law decay with an exponent that varies with $Δ$ and, for nonzero $Δ$, also with the width of the $λ_i$-distribution. The results for the transverse correlation function $ $ show a crossover from power-law decay to exponential decay as the exchange disorder is turned on.

cond-mat↗
arXiv1995

Impact of criticality and phase separation on the spin dynamics of the one-dimensional t-J model

The recursion method is used to determine the T=0 spin dynamic structure factor S_{zz}(q,ω) in the Luttinger liquid state and in the phase-separated state of the one-dimensional t-J model. As the exchange coupling increases from zero, the dispersions and line shapes of the dominant spin excitations are observed to undergo a major metamorphosis between the free-fermion limit and the onset of phase separation. The familiar two-spinon spectrum of the Heisenberg antiferromagnetic chain emerges gradually in the strongly phase-separated state.

cond-mat↗
arXiv1995

Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains

Dynamic spin correlation functions $ $ for the 1D $S=1/2$ $XX$ model $H = -JΣ_i \{S_i^x S_{i+1}^x + S_i^y S_{i+1}^y \}$ are calculated exactly for finite open chains with up to N=10000 spins. Over a certain time range the results are free of finite-size effects and thus represent correlation functions of an infinite chain (bulk regime) or a semi-infinite chain (boundary regime). In the bulk regime, the long-time asymptotic decay as inferred by extrapolation is Gaussian at $T=\infty$, exponential at $0 < T < \infty$, and power-law $(\sim t^{-1/2})$ at T=0, in agreement with exact results. In the boundary regime, a power-law decay obtains at all temperatures; the characteristic exponent is universal at T=0 $(\sim t^{-1})$ and at $0 < T < \infty$ $(\sim t^{-3/2})$, but is site-dependent at $T=\infty$. In the high-temperature regime $(T/J \gg 1)$ and in the low-temperature regime $(T/J \ll 1)$, crossovers between different decay laws can be observed in $ $. Additional crossovers are found between bulk-type and boundary-type decay for $i=j$ near the boundary, and between space-like and time-like behavior for $i \neq j$.

cond-mat↗