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We examine the dynamical magnetic response in a two-component resonating-valence-bond (RVB) description of the doped Mott insulator. The half-filled antiferromagnetic phase described by the Schwinger-boson mean-field theory will evolve into a bosonic-RVB state in the superconducting phase upon doping, where the doped holes introduce another fermionic itinerant spinon which forms a BCS-like RVB order. The spin excitations are thus composed of a resonance-like mode from the former and a weak dispersive mode from the itinerant component at the mean-field level. These two-component spinons are shown to give rise to an hourglass-like spin excitation at the RPA level via an antiferromagnetic coupling between the two modes, which provides an unconventional explanation of the experimental observations in the cuprate. In particular, we also discuss an instability towards an incommensurate magnetic order in this theoretical framework., 14 pages, 9 figures

Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from symmetry-protection of topological insulators to symmetry charge fractionalization on anyons in fractional quantum Hall effect. Topological phases in mixed quantum states, originating from decoherence in open quantum systems or disorders in imperfect crystalline solids, have recently garnered significant interest. Unlike pure states, mixed quantum states can exhibit average symmetries -- symmetries that keep the total ensemble invariant but not on each individual state. It was realized that symmetry-protected topological phases could be well-defined for such mixed states carrying average symmetries. In this work, we present a systematic classification and characterization of average symmetry-protected topological (ASPT) phases applicable to generic symmetry groups, encompassing both average and exact symmetries, for bosonic and fermionic systems. Moreover, we formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems. We demonstrate that numerous concepts from pure state symmetry-enriched topological (SET) phases, such as anyon permutation, symmetry fractionalization, and 't Hooft anomaly, are well-defined for ASET phases but with various intriguing twists. Our systematic approach helps clarify nuanced issues in previous literature and uncovers compelling new physics., 25 pages, 8 figures

We investigate the phase diagram at the boundary of an infinite two-dimensional cluster state subject to bulk measurements using tensor network methods. The state is subjected to uniform measurements $M = \cos{\theta}Z+\sin{\theta}X$ on the lower boundary qubits and all bulk qubits. Our results show that the boundary of the system exhibits volume-law entanglement at the measurement angle $\theta = \pi/2$ and area-law entanglement for any $\theta < \pi/2$. Within the area-law phase, a phase transition occurs at $\theta_c=1.371$. The phase with $\theta \in(\theta_c,\pi/2)$ is characterized by a non-injective matrix product state, which cannot be realized as the unique ground state of a 1D local, gapped Hamiltonian. Instead, it resembles a cat state with spontaneous symmetry breaking. These findings demonstrate that the phase diagram of the boundary of a two-dimensional system can be more intricate than that of a standard one-dimensional system., Comment: 7 pages, 6 figures

We propose a minimal interacting lattice model for two-dimensional class-D higher-order topological superconductors with no free-fermion realization. A Lieb-Schultz-Mattis-type constraint has been proposed and applied to guide our lattice model construction. Our model exhibits a trivial product ground state in the weakly interacting regime while increasing electron correlations provoke a novel topological quantum phase transition to a $D_4$-symmetric higher-order topological superconducting state. The symmetry-protected Majorana corner modes are numerically confirmed with the matrix-product-state technique. Our theory paves the way for studying correlated higher-order topology with explicit lattice model constructions., 11 pages, 6 figures

We design a strange correlator for the recently discovered average symmetry-protected topological (ASPT) phases in $1d$ and $2d$. The strange correlator has long-range or power-law behavior if the density matrix $\rho$ is in a nontrivial ASPT phase. In all the $2d$ cases considered here, we find interesting connections between strange correlators and correlation functions in $2d$ loop models, based on which we can extract exact scaling exponents of the strange correlators., Comment: 10 pages, 5 figures. Comments are welcome!

The notion of higher-order topological phases can have interesting generalizations to systems with subsystem symmetries that exhibit fractonic dynamics for charged excitations. In this work, we systematically study the higher-order topological phases protected by a combination of subsystem symmetries and ordinary global symmetries in two and three-dimensional interacting boson systems, with some interacting fermionic examples., 17 pages, 4 figures with references, comments are welcome!

The boundary of topological phases of matter can manifest its topology nature, which leads to the so-called boundary-bulk correspondence (BBC) of topological phases. In this Letter, we construct a one-to-one correspondence between the boundary theories of fermionic SPT (fSPT) phases protected by crystalline symmetry and on-site symmetry in 2D fermionic systems, which follow the so-called crystalline equivalence principle. We dub such correspondence crystalline equivalent BBC. We illustrate this correspondence by two simple examples and as an application, we discover the topological boundary theory of 2D fSPT phase with spin-1/2 fermions, protected by a non-Abelian group $\mathbb{Z}_4\rtimes\mathbb{Z}_2^T$ with $A^4=\mathcal{T}^2=P_f$ where $A$ is the generator of $\mathbb{Z}_4$, from its crystalline equivalent partner -- 2D higher-order fSPT phase with spinless fermions, protected by $D_4$ symmetry., 4+epsilon pages, 3 figures, with supplementary materials. Comments are welcome

We investigate the tensor network representations of fermionic crystalline symmetry-protected topological (SPT) phases on two-dimensional lattices. As a mapping from virtual indices to physical indices, projected entangled-pair state (PEPS) serves as a concrete way to construct the wavefunctions of 2D crystalline fermionic SPT (fSPT) phases protected by 17 wallpaper group symmetries, for both spinless and spin-1/2 fermions. Based on PEPS, the full classification of 2D crystalline fSPT phases with wallpaper groups can be obtained. Tensor network states provide a natural framework for studying 2D crystalline fSPT phases., 12 figures, 3 tables, comments are welcome

Influence of the combined effect of ultra-sonication (US) and high-voltage cold plasma treatment (HVCP) on the quality parameters of fresh carrot juice has been studied. During the treatment of ultra-sonication, carrot juice was subjected to a 0.5 inch probe for 3 min by adjusting the pulse duration 5 s on and off at 20 kHz frequency, amplitude level 80%. The ultrasound intensity was measured by using a thermocouple and was 46 Wcm&minus, 2. The temperature was maintained at 10 &deg, C by an automatic control unit. During the treatment of HVCP, carrot juice was then subjected to dielectric barrier discharge (DBD) plasma discharge at 70 kV voltage for 4 min. Significant increases were observed when HVCP treated carrot juice was tested against total carotenoids, lycopene, and lutein when compared to the control treatments. Moreover, this increase was raised to its highest in all pigments, chlorogenic acid, sugar contents, and mineral profile, as the results of ultra-sonication when combined with high voltage atmospheric cold plasma (US-HVCP). Whereas, a significant decreased was observed in Mg, total plate count, yeast, and mold after US-HVCP treatment. Furthermore, results indicated that the combined effect of US-HVCP treatment has improved the quality and led to a higher concentration of lycopene, lutein, chlorogenic acid, and mineral compounds (Na, K, and P). Therefore, the findings of the current study suggested that US-HVCP treatment is a novel combined technique that could provide better quality and more stability during the processing of carrot juice with better physicochemical properties and bio-available nutrients, so this novel processing technique could serve as an alternative to traditional processes.

The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction of space group SPT phases were also proposed for interacting bosonic systems. In this paper, we attempt to generalize this classification and construction scheme systematically into interacting fermion systems. In particular, we construct and classify point group SPT phases for 2D interacting fermion systems via lower-dimensional block-state decorations. We discover several intriguing fermionic SPT states that can only be realized in interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, the potential experimental realization of these new classes of point group SPT phases in 2D correlated superconductors is addressed., 4+epsilon pages, 4 figures, 2 tables; with supplementary material; Published version