We study theoretically a driven dissipative one-dimensional XXZ spin-1/2 chain with dipole coupling and a tunable strength of the Ising and XY interaction. Within a mean-field approximation, we find a rich phase diagram with uniform, spin density wave, antiferromagnetic and oscillatory phases, as well as regions of phase bistability. We study the phase diagram of small quantum systems using exact diagonalisation, and compare the results to the mean-field theory. We find that while expectation values only capture the uniform phases of the mean-field theory, fluctuations about these expectation values give signatures of spatially non-uniform phases and bistabilities. We find these signatures for all ratios of the Ising to XY interaction, showing that they appear to be general features of spin-1/2 systems.
We study a driven-dissipative model of spins one-half (qubits) on a lattice with nearest-neighbor interactions. Focusing on the role of spatially extended spin-spin correlations in determining the phases of the system, we characterize the spatial structure of the correlations in the steady state, as well as their temporal dynamics. In dimension one we use essentially exact matrix-product-operator simulations on large systems, and pushing these calculations to dimension two, we obtain accurate results on small cylinders. We also employ an approximation scheme based on solving the dynamics of the mean field dressed by the feedback of quantum fluctuations at leading order. This approach allows us to study the effect of correlations in large lattices with over one hundred thousand spins, as the spatial dimension is increased up to five. In dimension two and higher we find two new states that are stabilized by quantum correlations and do not exist in the mean-field limit of the model. One of these is a steady state with mean magnetization values that lie between the two bistable mean-field values and whose correlation functions have properties reminiscent of both. The correlation length of the new phase diverges at a critical point, beyond which we find emerging a new limit cycle state with the magnetization and correlators oscillating periodically in time.
We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, which exhibits a second order phase transition. All our results compare well with the predictions from a dissipative
ϕ4 field theory.
A quantum many-body system coupled to an environment relaxes to a nonequilibrium steady state that can sustain order with no equilibrium counterpart. Computing such steady states is harder than closed-system dynamics as the density matrix problem squares the Hilbert-space dimension, and no free energy selects the steady state. The dissipative spin-1/2 Heisenberg chain is a benchmark example for nonequilibrium steady state physics; various methods have each calculated its phase diagram but do not agree, and a controlled determination at large system size has remained out of reach. Here we simulate the Lindblad dynamics of chains of up to 50 sites on the superconducting processor ibm_kingston -- 100 simultaneously active qubits at up to 1700 entangling-gate depths -- realizing the dissipation via Stinespring dilation. The system's dissipative evolution is a self-correcting mechanism that effectively erases errors, so hardware noise enters only as a weak competing dissipator. We measure static structure factors and resolve ferromagnetic, antiferromagnetic, spin-density-wave, and paramagnetic steady states, mapping the phase diagram with 117 quantum hardware data points across the
Jx--
Jy plane. We uncover a rich non-equilibrium phase diagram of ordered phases with only remnants of the mean-field order, and where sharp transitions give way to the crossovers expected in one dimension. We also find the existence of an incipient (Trotter-induced) spin density wave phase, highlighting the potential of controlled Trotterization as a tool to engineer various magnetic phases in dissipative spin systems. Our quantum simulations largely settle the lingering uncertainty regarding the correct phase diagram of this benchmark system. Moreover, they show that quantum computers are now a feasible tool for addressing scientific questions involving dissipative quantum systems.
We investigate the steady-state phase diagram of the dissipative spin-1/2 XYZ model on a two-dimensional triangular lattice, in which each site is coupled to a local environment. By means of cluster mean-field approximation, we find that the steady-state phases of the system are rather rich, in particular there exist various types of nonuniform antiferromagnetic phases due to the geometrical frustration. As the short-range correlations are included in the analysis, the numerical results show that the oscillatory phase disappears while the triantiferromagnetic and biantiferromagnetic phases remain to exist in the thermodynamic limit. Moreover, the existence of the spin-density-wave phase, which is missed by the single-site mean-field analysis, is also revealed by the spin-structure factor.
We revisit the phase diagram of the dimerized XXZ spin-
21 chain with nearest-neighbor couplings which was studied numerically in Phys. Rev. B 106, L201106 (2022). The model has isotropic
XY couplings which have a uniform value and
ZZ couplings which have a dimerized form, with strengths
Ja and
Jb on alternate bonds. We find a rich phase diagram in the region of positive
Ja, Jb. We provide a detailed understanding of the different phases and associated quantum phase transitions using a combination of mean-field theory, low-energy effective Hamiltonians, renormalization group calculations employing the technique of bosonization, and numerical calculations using the density-matrix renormalization group (DMRG) method. The phase diagram consists of two Ising paramagnetic phases called IPM
0 and IPM
π, and a phase with Ising Neel order called IN; all these phases are gapped. The phases IPM
0 and IPM
π are separated by a gapless phase transition line given by
0≤Ja=Jb≤1 which is described by a conformal field theory with central charge
c=1. There are two gapless phase transition lines separating IPM
0 from IN and IPM
π from IN; these are described by conformal field theories with
c=21 corresponding to quantum Ising transitions. The
c=1 line bifurcates into the two
c=21 lines at the point
Ja=Jb=1; the shape of the bifurcation is found analytically using RG calculations. A symmetry analysis shows that IPM
0 is a topologically trivial phase while IPM
π is a time-reversal symmetry-protected topological phase (SPT) with spin-
21 states at the two ends of an open system. The numerical results obtained by the DMRG method are in good agreement with the analytical results. Finally we propose experimental platforms for testing our results.