Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCPs) in a nontrivial way.As was pointed out in the recent literature on (1 + 1)d conformal field theory (CFT) [Garratt et al.Measurements conspire nonlocally to restructure critical quantum states, arXiv:2207.09476(2022)], the effect of weak measurement can be mathematically mapped to the problem of boundary CFT.In this work, we focus on the (2 + 1)d QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently.We focus on decoherence caused by weak measurements with and without postselecting the measurement outcomes.Our main results are as follows: (1) for an O(N ) Wilson-Fisher QCP under weak measurement with postselection, an observer would, in general, observe two different types of boundary and defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic "extraordinary-log" correlation.(2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy.We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model.(3) When there is no postselection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the "disorder operator" would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement.
Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCPs) in a nontrivial way.As was pointed out in the recent literature on (1 + 1)d conformal field theory (CFT) [Garratt et al.Measurements conspire nonlocally to restructure critical quantum states, arXiv:2207.09476(2022)], the effect of weak measurement can be mathematically mapped to the problem of boundary CFT.In this work, we focus on the (2 + 1)d QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently.We focus on decoherence caused by weak measurements with and without postselecting the measurement outcomes.Our main results are as follows: (1) for an O(N ) Wilson-Fisher QCP under weak measurement with postselection, an observer would, in general, observe two different types of boundary and defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic "extraordinary-log" correlation.(2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy.We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model.(3) When there is no postselection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the "disorder operator" would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement.
Measurements are usually introduced as probes of quantum systems, but they can also act as a powerful, intrinsically nonunitary control knob for manipulating quantum states. This thesis develops the theory, experimental realization, and detection of measurement-altered quantum criticality in one-dimension: the phenomenon where local measurements on critical wave functions reshape universal long-distance correlations, entanglement, and other scaling behaviors. We show that measurements generate defect or boundary perturbations in the underlying conformal field theory, producing new measurement-induced fixed points and new universal observables that are often invisible to the pristine theory. In transverse-field Ising chains, we design measurement-altered criticality protocols in which correlated ancillas are entangled with the critical system and then projectively measured. This setting shows that measurement basis, entangling gate, measurement outcome, and ancilla correlations can qualitatively change correlations in the system and induce outcome-dependent order-parameter condensation. We also develop nonstandard probes --- including higher moments and symmetry-resolved averages --- that retain nontrivial signatures of the post-measurement ensemble. These ideas are then connected to quantum information by studying imperfect teleportation of critical many-body wavefunctions. Teleportation errors can be reinterpreted as effective weak measurements acting on an otherwise faithfully teleported critical state. This perspective yields a classification of protocols in which imperfections either preserve universal correlations and entanglement scaling, continuously deform them, or destroy long-range entanglement while leaving altered power-law correlations behind. Measurement-altered criticality therefore becomes not only a fundamental phenomenon, but also a tool for understanding and optimizing noisy quantum-information protocols. We also broaden the framework to measurement-induced boundary physics. In a gapless parent of the one-dimensional cluster state, a single round of measurements can generate boundary conformal field theories with distinct universal properties. Rotating the measurement basis drives transitions between these boundary fixed points, producing measurement-induced boundary transitions that have no analogue in the descendant gapped cluster state. Extensions to tricritical Ising and three-state Potts criticality show that such transitions arise generally in 1+1D conformal field theories. Finally, the thesis addresses experimental access. We propose practical protocols for observing measurement-altered criticality in Rydberg atom arrays tuned to Ising and tricritical-Ising transitions, where projective measurements of selected atoms can controllably modify critical correlations with experimentally favorable post-selection probabilities. We also develop a post-selection-free framework for extracting nonlinear observables from raw measurement records using statistical learning. By recasting higher moments of conditioned observables as supervised learning objectives, the method replaces exponentially costly sector-by-sector postselection with regression whose sample complexity is controlled by decoder capacity. In critical Ising chains, linear, logistic, and convolutional decoders recover measurement-altered scaling and correlations from simulated unpostselected data. Together, these results establish measurements as a practical and universal route to engineering, diagnosing, and exploiting new forms of quantum critical behavior.
This dissertation is devoted to the study of universal observables in quantum critical systems, most of which have a non-local character. The overarching goal of this work is to compute new universal observables of critical points to aid theoretical understanding of these systems.\nWe first consider the finite-size energy spectrum of quantum critical points on the torus. We compute the spectrum for the Wilson-Fisher conformal field theory in the epsilon=3−d expansion, where the energy spectrum maps onto a strongly-coupled problem in quantum mechanics. We also compute the energy spectrum to leading order in 1/N, and we compare the two expansions. We then study the torus spectra associated with a class of confinement transitions in states with mathbbZ2 topological order. After introducing these universality classes, we show that the critical torus spectrum can be used to detect nontrivial effects like spontaneous symmetry breaking and emergent gauge degrees of freedom. We compare our analytic results with numerical simulations where available, demonstrating the utility of the torus spectrum as a useful characterization of the universality class of a quantum critical point.\nWe then present a computation of the von Neumann entanglement entropy of the Wilson-Fisher and Gross-Neveu conformal field theories in the large N limit. We obtain an exact mapping to the von Neumann entanglement entropy of a free quantum field theory, allowing an exact determination of the entanglement entropy in a number of cases. \nWe also study a critical point displaying impurity-driven critical behavior in a boson superfluid-insulator phase transition. The presence of an impurity drives the system to a new interacting universality class, which has critical exponents associated with the scaling dimensions of the impurity degree of freedom. We present the universal quantum field theory of this transition and compute the critical exponents and finite-temperature compressibility at the critical point using the epsilon expansion.
We analyze the effect of decoherence, modeled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "g function" in conformal field theory, allowing us to define a notion of renormalization group (RG) flow (or "phase transitions") between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the conformal field theory. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods.
Modern quantum platforms naturally realize many-body states shaped by measurement, decoherence, and dissipation. The appropriate object is often not a wave function or ground state, but a density matrix. This thesis asks how phases and phase transitions can be defined for such mixed states, especially when universal structure appears only through nonlinear, replicated, or doubled diagnostics. The thesis develops this perspective using nonlinear diagnostics, doubled-Hilbert- space representations, statistical-mechanics mappings, and generalized symmetry. It shows that weak measurement can suppress higher-form symmetry breaking and drive mixed-state transitions; maps fidelity diagnostics of decohered Chern insulators to effective conformal-field-theory partition functions; and maps Rényi diagnostics of noisy stabilizer and CSS codes to dual statistical-mechanics models connected to decodability. It also shows that measurement and Lindbladian evolution can prepare density matrices whose doubled-space representations realize spin-liquid-like states and superconducting order. Finally, it identifies strong-to-weak symmetry breaking as a route to universal mixed-state behavior connected to hydrodynamic emergence. Together, these results show that openness is not only a perturbation that degrades pure-state physics. Measurement, decoherence, and dissipation can hide, preserve, trans- form, or generate structure in density matrices. The resulting phases and transitions are tied to information processing: what can be decoded, distinguished, recovered, or lost to local probes.
In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin 1/2 system with next-nearest-neighbour exchange interactions(K), which shows analogues phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction Kc and in the valance bond solid phase above Kc. The weak measurement is carried out by coupling a secondary ancilla system to the critical system via unitary interactions and later measuring the ancilla spins projectively. We numerically calculate entanglement entropy,correlation length, and order parameters of leading post-measurement states using uniform matrix product state representation of the quantum many-body state in the thermodynamic limit. We report asymmetric restructuring of entanglement of the post measurement states across the phase boundary under weak measurements. Especially, the trajectory (↓↓) describing a uniform measurement outcome given the all ancilla spins initiated in the same (↓) state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when K<Kc whereas it weakly decreases when K>Kc. We argue with numerical evidences that observed asymmetry in entanglement would lead to a weak first order phase boundary in the thermodynamic limit. We also discuss important aspects in experimental observation of measurement induced effects linked to the strength of weak measurement and probability of post-measurement states.
The fermion disorder operator has been shown to reveal the entanglement information in 1D Luttinger liquids and 2D free and interacting Fermi and non-Fermi liquids emerging at quantum critical points (QCPs) [W. Jiang et al., arXiv:2209.07103]. Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of the disorder operator in correlated Dirac systems. We first demonstrate the logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN) chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT) content of the GN-QCP in its coefficient is found. Then we study a 2D monopole-free deconfined quantum critical point (DQCP) realized between a quantum-spin Hall insulator and a superconductor. Our data point to negative values of the logarithmic coefficients such that the DQCP does not correspond to a unitary CFT. Density matrix renormalization group calculations of the disorder operator on a 1D DQCP model also detect emergent continuous symmetries.