We study the zero-temperature critical behavior of dissipative quantum Ising spin chains of finite and infinite length. The spins interact with either constant or random nearest-neighbor ferro-magnetic couplings. They are also subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system performing Monte Carlo simulations on a classical two-dimensional counterpart model. We find that the coupling to the bath enhances the extent of the ordered phase, as it is known for mean-field spin-glass models. In the case of finite chains we show that a generalization of the Caldeira-Leggett localization transition exists.
We consider a prototypical system of an infinite range transverse field Ising model coupled to a bosonic bath. By integrating out the bosonic degrees, an effective anisotropic Heisenberg model is obtained for the spin system. The phase diagram of the latter is calculated as a function of coupling to the heat bath and the transverse magnetic field. Collective excitations at low temeratures are assessed within a spin-wave like analysis that exhibits a vanishing energy gap at the quantum critical point. We also consider another limit where the system reduces to a generalized spin-boson model of two interacting spins. By increasing the coupling strength with the heat bath, the two-spin wavefunction changes from an entangled state to a factorized state of two spins which are aligned along the transverse field. We also discuss the possible realization and application of the model to different physical systems.
Abstract We study the critical properties of finite-dimensional dissipative quantum spin systems with uniform ferromagnetic interactions. Starting from the transverse field Ising model coupled to a bath of harmonic oscillators with Ohmic spectral density, we generalize its classical representation to classical spin systems with O ( n ) symmetry and then take the large- n limit to reduce the system to a spherical model. The exact solution to the resulting spherical model with long-range interactions along the imaginary time axis shows a phase transition with static critical exponents coinciding with those of the conventional short-range spherical model in d + 2 dimensions, where d is the spatial dimensionality of the original quantum system. This implies that the dynamical exponent is z = 2. These conclusions are consistent with the results of Monte Carlo simulations and renormalization group calculations for dissipative transverse field Ising and O ( n ) models in one and two dimensions. The present approach therefore serves as a useful tool for analytically investigating the properties of quantum phase transitions of the dissipative transverse field Ising and other related models. Our method may also offer a platform to study more complex phase transitions in dissipative finite-dimensional quantum spin systems, which have recently received renewed interest in the context of quantum annealing in a noisy environment.
We show that tailoring the dissipative environment allows us to change the features of continuous quantum phase transitions and even induce first-order transitions in ferromagnetic spin chains. In particular, using a numerically exact quantum Monte Carlo method for the paradigmatic Ising chain of one-half spins in a transverse magnetic field, we find that spin couplings to local quantum boson baths (in the Ohmic regime) can drive the transition from the second to the first order even for a low dissipation strength. Moreover, using a variational mean-field approach for the treatment of spin-spin and spin-boson interactions, we point out that phase discontinuities are ascribable to a dissipation-induced effective magnetic field which is intrinsically related to the bath quantum fluctuations and vanishes for classical baths. The effective field is able to switch the sign of the magnetization along the direction of spin-spin interactions. The results can be potentially tested in recent quantum simulators and are relevant for quantum sensing since the spin system could not only detect the properties of nonclassical baths, but also the effects of weak magnetic fields.
We investigate the critical behavior of a spin chain coupled to bosonic baths characterized by a spectral density proportional to ${\ensuremath{\omega}}^{s}$, with
s>1. Varying
s changes the effective dimension
deff=d+z of the system, where
z is the dynamical critical exponent and the number of spatial dimensions
d is set to one. We consider two extreme cases of clock models, namely Ising-like and
U(1)-symmetric ones, and find the critical exponents using Monte Carlo methods. The dynamical critical exponent and the anomalous scaling dimension $\ensuremath{\eta}$ are independent of the order parameter symmetry for all values of
s. The dynamical critical exponent varies continuously from $z\ensuremath{\approx}2$ for
s=1 to
z=1 for
s=2, and the anomalous scaling dimension evolves correspondingly from $\ensuremath{\eta}\ensuremath{\gtrsim}0$ to $\ensuremath{\eta}=1/4$. The latter exponent values are readily understood from the effective dimensionality of the system, being ${d}_{\mathrm{eff}}\ensuremath{\approx}3$ for
s=1, while for
s=2 the anomalous dimension takes the well-known exact value for the two-dimensional Ising and
XY models, since then
deff=2. However, a noteworthy feature is that
z approaches unity and $\ensuremath{\eta}$ approaches
1/4 for values of
s<2, while naive scaling would predict the dissipation to become irrelevant for
s=2. Instead, we find that $z=1,\ensuremath{\eta}=1/4$ for $s\ensuremath{\approx}1.75$ for both Ising-like and
U(1) order parameter symmetry. These results lead us to conjecture that for all site-dissipative
Zq chains, these two exponents are related by the scaling relation $z=\mathrm{max}{(2\ensuremath{-}\ensuremath{\eta})/s,1}$. We also connect our results to quantum criticality in nondissipative spin chains with long-range spatial interactions.