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.
Motivated by experiments on spin chains embedded in a metallic bath, as well as closed quantum systems described by long-range interacting Hamiltonians, we study a critical
SU(N) spin chain perturbed by dissipation, or equivalently, after space-time rotation, long-range spatial interactions. The interplay of dissipation and the Wess-Zumino (Berry phase) term results in a rich phase diagram with multiple renormalization-group fixed points. For a range of the exponent that characterizes the dissipative bath, we find a second-order phase transition between the fixed point that describes an isolated critical spin chain and a dissipation-induced-ordered phase. More interestingly, for a different range of the exponent, we find a stable, gapless, nonrelativistic phase of matter whose existence necessarily requires coupling to the dissipative bath. Upon tuning the exponent, we find that the fixed point corresponding to this gapless, stable phase ``annihilates'' the fixed point that describes the transition out of this phase to the ordered phase. We also study a relativistic version of our model, and we identify a new critical point. We discuss the implications of our work for Kondo lattice systems and engineered long-range interacting quantum systems.
We consider an S=1/2 antiferromagnetic quantum Heisenberg chain where each site is coupled to an independent bosonic bath with ohmic dissipation. The coupling to the bath preserves the global SO(3) spin symmetry. Using large-scale, approximation-free quantum Monte Carlo simulations, we show that any finite coupling to the bath suffices to stabilize long-range antiferromagnetic order. This is in stark contrast to the isolated Heisenberg chain where spontaneous breaking of the SO(3) symmetry is forbidden by the Mermin-Wagner theorem. A linear spin-wave theory analysis confirms that the memory of the bath and the concomitant retarded interaction stabilize the order. For the Heisenberg chain, the ohmic bath is a marginal perturbation so that exponentially large system sizes are required to observe long-range order at small couplings. Below this length scale, our numerics is dominated by a crossover regime where spin correlations show different power-law behaviors in space and time. We discuss the experimental relevance of this crossover phenomena.
Open quantum spin systems offer a previously unexplored route to realizing deconfined quantum criticality. We consider a spin-1/2
J-
Q3 chain, consisting of an antiferromagnetic (AFM) Heisenberg exchange and a competing multi-spin interaction favoring a valence-bond solid (VBS) state, with each spin component coupled to a bosonic bath. Using non-Abelian bosonization and renormalization-group (RG) analysis, combined with large-scale quantum Monte Carlo (QMC) simulations, we determine the phase diagram and the associated phase transitions of the model. We show that strong dissipation stabilizes an AFM phase for sub-Ohmic, Ohmic, and super-Ohmic baths. Continuous AFM-VBS transitions at finite dissipation are found upon increasing the multi-spin interaction in both the sub-Ohmic and Ohmic regimes. Critical properties are obtained through perturbative RG analysis and QMC simulations. In the Ohmic case, the critical point features spinon deconfinement and emergent O(4) symmetry. In the sub-Ohmic regime, the transition may also involve spinon deconfinement, provided that spinons remain deconfined in the dissipative VBS phase. In addition, in the super-Ohmic regime, we propose a transition from AFM phase to a quasi-long-range ordered phase.
We study the effect of bond dissipation on the one-dimensional antiferromagnetic spin-
1/2 Heisenberg model. In analogy to the spin-Peierls problem, the dissipative bath is described by local harmonic oscillators that modulate the spin exchange coupling, but instead of a single boson frequency we consider a continuous bath spectrum
∝ωs. Using an exact quantum Monte Carlo method for retarded interactions, we show that for
s<1 any finite coupling to the bath induces valence-bond-solid order, whereas for
s>1 the critical phase of the isolated chain remains stable up to a finite critical coupling. We find that, even in the presence of the gapless bosonic spectrum, the spin-triplet gap remains well defined for any system size, from which we extract a dynamical critical exponent of
z=1. We provide evidence for a Berezinskii-Kosterlitz-Thouless quantum phase transition that is governed by the SU(2)
1 Wess-Zumino-Witten model. Our results suggest that the critical properties of the dissipative system are the same as for the spin-Peierls model, irrespective of the different interaction range, i.e., power-law vs. exponential decay, of the retarded dimer-dimer interaction, indicating that the spin-Peierls criticality is robust with respect to the bosonic density of states.